What is the difference between "hi" and "low" input jacks on guitar / bass amps? Usually bigger amps have both of them (didn't see them on smaller ones really)..
The "Hi" input attenuates the input signal, usually by between 10-15dB (about half to a third the original volume). The "Low" input will not do this.
Different guitars and basses produce widely varying signal levels. This isn't just a passive vs active thing; plug a vintage-voiced Strat into the amp, then a PAF-voiced Les Paul; you'll have to turn the gain down. By contrast, the preamp of your amplifier works best with a signal in a particular range of strength; too hot, and you'll clip the preamp (which is generally not the best sound especially if you want a clean tone). Too low, and subtleties of tone become lost in the amp circuitry's "noise floor".
The different inputs, or the attenutation switch on a single input, allows you to "turn down" a hot guitar with a simple switch instead of involving other elements of the preamp. This has two benefits, both tied to being able to turn the other "downstream" controls to higher levels. First, taming a hot signal without an attenuator usually requires turning down the "Pre Gain" level. This knob, especially on a tube amp, will become very sensitive; small moves will produce huge volume changes. By attenuating the signal before this point in the circuit, the knob becomes less sensitive to small moves. Second, by allowing controls like the pre-gain to be turned higher, more of the original "native tones" of the instrument get into the preamp stage, and the tone and equalization controls have more to work with. Overall, this results in a "less muddy" sound, as subtle harmonics and overtones aren't lost in the noise floor of the amp.
Contrary to what the previous answers stated, the different sensitivity is not the primary difference between the "hi" and "lo" inputs. It is indeed different, usually by 6 dB, but you could achieve this with the gain knob alone.
More important is the different impedance of both inputs: a "hi" input has a very high inner electric resistance (in the range of 1 MΩ), that is, it accepts the voltage the guitar outputs while there needs to be hardly any current at all. The guitar pickups can then do their job (which is translating the string vibrations to electrical voltages) completely freely without having to also supply a lot of current; so they can do a lot of resonance, which gives a bright and open, but sometimes also annoying and "un-compact" sound.
A "lo" input, on the other hand, typically has an impedance of about 150 kΩ, roughly 1/7th of the hi input's. That means, when the pickups try to send their voltage to the amp there will always be a significant current the pickups also have to supply. Actually, it's still a very small current – something like fractions of microamperes – but guitar pickups are very weak sources of current. Voltage and current together means they need to push energy to the amp: this energy will be taken from their own high-frequency resonances, therefore a normal electric guitar will sound more mellow when plugged into the "lo" input than when it's plugged into the "hi" input. It will also be simply quiter because of the attenuation, but this, as I said, is less important.
Every pickup responds differently to the amp impedance: some will sound muffled and dull when plugged into a "lo" input, others shrill and disturbing with a "hi" input. So when you're using two different guitars live, it can sometimes be useful to use each input for one of them (you should still always unplug the one you're not playing from the amp).
They assume different signal levels so have different levels of gain in the pre-amp. In fact on some amps the low input has a pre-amp but the high just goes directly into the main amp.
This is to cope with the fact that instruments can have very different output signal levels, but it can also be used to change the tone of the sound produced.
On my Ampeg amp, the instructions said that if you are playing a bass with passive pickup(s), to plug into the 0db jack; and if your bass has active pickups, to use the -15db jack.
Hmmm. An oldish thread but thought I would comment. If you look at the schematic for the Marshall JCM 800 Lead Series (http://drtube.com/schematics/marshall/jcm800pr.gif) you can see the guitar inputs marked 'High' and 'Low' on the top left of the schematic. First of all, those 68K resistors. They are there for damping radio frequency (RF) interference. They are called "grid stopper resistors" and all tube amps have them on the inputs from the external world. They prevent RF from getting onto the grid of the tube and being amplified. Although you won't be able to hear it, it will chew up power unnecessarily. The exact value is not important.
Some amplifiers use these grid stopper resistors for other purposes - as in the case of the JCM 800 while some do not. You can tell if these resistors are doubling up for other purposes by where they are connected. If they are the only component connected to the grid (see the TSL60 for an example - same website as above) they are not being used for other purposes; if not the only component connected to the grid, they are being used for dual purposes - as in the case of the JCM 800.
Lets take the High input. If you plug your guitar into that input (and nothing in the Low input), the impedance seen by the guitar is 1 megohm (see that resistor to ground marked 1M). The two 68K resistors in parallel (34K) are in series with the guitar and the grid. Since the impedance into the grid is infinite, no current flows through those resistors and the signal seen by the grid is exactly the same as the top end of the 1M resistor. That is, 100% of the guitar signal is applied to the grid. Summarising, this "High" input has an impedance of 1M and no attenuation of the guitar signal.
Now consider the "Low" input (with nothing plugged into the High input). Now you have two 68K resistors in series to ground so the input impedance seen by the guitar will be 136K. The connection to the grid occurs at the midpoint of these two resistors therefore the signal on the grid is one half of the signal generated by the guitar - in other words, -6dB (for voltage, attenuation of one half is a 6dB cut, for power an attenuation of one half is a 3dB cut). This input has one of the 68K resistors in series with the grid so it will have slightly different RF characteristics but this is of no consequence. Summarising, the "Low" input has an impedance of 136K and cuts the signal by 6dB. This "Low" input will also present a different sonic result because of the lower impedance. The higher the internal impedance of the guitar, the more noticeable this will be.
So, what does all this mean as asked by the OP?
If you plug exactly the same guitar into each input in turn, the "Low" input will yield a lower internal signal level - 6dB lower as noted above. The sound may well have less high-end but this depends on the guitar as well. Conversely, the "High" input will give you a stronger internal signal and, possibly, more high-end. Therefore, you are more likely, but not obligated, to plug a high-output guitar into the "Low" input and vice versa.
With one extra resistor, Marshall could have built this amp with similar impedance on both inputs, distinguished only by the amount of attenuation but they didn't. I wonder why.
If you now look at the Marshall VBA4-60 (http://drtube.com/schematics/marshall/vba4-60-00.pdf) you can see the same basic concept but the inputs are labelled "Passive" and "Active." Active pickup guitars will have a higher signal output and lower output impedance than passive but I doubt that this was the reason why the JCM-800 was built the way it is. Finally, you can see that 1 Megohm resistor in the VBA4-60 as well as the JCM-800. What is it there for? If you took it away, the input impedance of the amp would be much, much higher which should be a good thing, yes? Well, sadly, if you took it away the amplifier would stop working after a while. Tubes are not perfect and there is a very small leakage current that comes out of the grid connection. The 1M resistor provides a path to ground for this current. Without it, charge would build up on the grid and eventually pinch-off the signal....
The reason active pickups have low impedance and passive pickups have high impedance is because active pickups (usually a misnomer meaning "passive pickups and an on-board amplifier circuit tailored to the pickups") use a power source to transform the naturally high impedance of the pickup coil into a low impedance.
This is the same way a buffer pedal works, btw. A buffer pedal will transform high impedance sources into a low impedance source while retaining the same signal level (voltage). But how does a buffer pedal work? A wallwart or a 9v. You need a second source of power to transform output impedance from high to low.
So if you want to use a passive pickup guitar with no on board electronics in a low impedance input for whatever reason, you can use a buffer pedal to do it.
High = high impedance. Low = low impedance.
The way the signal works is like this: https://learn.sparkfun.com/tutorials/voltage-dividers
Essentially, if your SourceImpedance (pickups, pedal) is 10, and your Load Impedance (the input of the amplifier) is 10, then you've cut your voltage in half in DC voltage terms.
But it doesn't end there. Since impedance acts like a different size of resistance based on what AC frequency rolls through, then it also has an effect on tone.
You might find that you want to use a high impedance input even with active pickups because it gives you a basic tone you want to shape with guitar or amp tone controls. Or you might prefer the basic tone that comes from the low input.
If the high input causes your guitar to drive the amp too hard, you can use the low input or turn your guitar down (which also has an effect on tone since it rolls off highs harder than lows).
This is incidentally why some guitar amps that don't have both types of inputs have a "tone cut" switch on them.
Use the input that sounds good to you, what you need to get you to the breakup/distortion level vs loudness you want. Some passive pickups in a low impedance can probably let you turn the amp up to 10 before it starts getting a some breakup. On the other hand, an active pickup guitar plugged into the high might not get up to with the amp volume before it starts breaking up.
Always be experimenting.