What is true bypass on a pedal? What are it's advantages? What are it's disadvantages?
Every effect pedal, when on, runs your guitar's signal through its effect circuitry, which produces the altered signal. Fine. But what about when the pedal is off? Doesn't your guitar's signal just pass through the pedal unaffected?
Actually, in many (most?) pedals, the answer is no. For these pedals---which include everything made by DOD, Boss, Ibanez, and most of the other pedals you'd find at Guitar Center---run the guitar's signal through a buffer amp. This amp is supposed to be as clean as possible and is designed to change the signal as little as possible, but it's not 100% transparent. Your guitar's sound will be ever-so-slightly affected by the buffer amp in the pedal, even when it's not engaged.
The buffer amp is there to prevent potential signal loss if you have a long chain of effects. If you have, say, six or seven effects pedals, you're adding many feet of additional cable length between your guitar and the amp. Because the guitar's signal is high-impedance, long cable lengths have the potential to rob the signal of some of the high frequencies (this isn't an issue with low-impedance signals, which is why microphones can run through cables of 100' or more, while guitar cables should really be 30' or less.), and your tone can suffer. The buffer amp performs some impedance matching so that the signal stays true even through long cable lengths.
"True bypass" means the pedal doesn't have this buffer amp, and passes the signal straight through from input to output with no circuitry in between. This means it has the greatest possible fidelity to the original guitar signal; basically, when disengaged the pedal is no different than an extension of the guitar cable. Usually you see this feature in high-end boutique pedals.
This article by Dunlop does a great job of explaining true bypass, buffer amps, and the other issues involved in bypassing effects.
The real problem with true bypass originates with the LED and the nature of the stomp switch.
Generally (meaning without taking into account clever things like the RAT bypass) a true bypass requires an entire "double pole, double throw" (DPDT) switch. One pole is used to direct where the input signal goes - either to the circuit or directly to the output. The other is used to determine where the output comes from - either the circuit or straight from the input. That's fine, because that common button push-down, clicky switch that you step on just happens to be DPDT (at least on older pedals).
However, as soon as you add an LED that switches on and off when you step on the switch, everything changes. The LED needs it's own isolated circuit that's connected to the switch. That takes up one of the poles on the DPDT switch, which makes simple true bypass impossible.
The original strategy was to leave the input connected to one of the switch poles, but to have the output permanently connected to both the circuit output and the input pole's "off" selection. The idea being that when the switch is in the off position, then there's no signal going to the input of the circuit and therefore nothing coming out of it.
The problem with that is that although there's no signal coming out of the circuit when the switch is in the off position, the circuit is still connected to ground and therefore some of the "bypassed" signal at the output can travel backwards up the circuit to the ground. Depending on the stompbox circuit, different frequencies will get drained away in this manner resulting the dreaded "tone suck".
In modern stompbox design this is no longer an issue. Why? The triple pole double throw (3PDT) stompbox switch, while not a new invention, is now dirt cheap. 10 years ago, a 3PDT footswitch would have cost about $15, while a DPDT switch cost around $3. And they were as rare as hens' teeth. Today, they cost about $4 and will probably be easier to source than DPDT switches in the near future. So now even the cheapest mass manufactured stompboxes can be built with true bypass.
So back when true bypass was an issue, most of the big manufacturers moved to buffered circuits. Simply put, a buffer is a unity gain amplifier (meaning that it does make the signal any louder or softer) that isolates the input from the output and transforms the signal from high impedance to low impedance. Generally, low impedance signals are much more resilient to "tone suck" than high impedance signals. However, some claim that having a whole bunch of buffered pedals daisy chained to each other has a "tone such" effect all its own.
Basically in short, if an effect/pedal is said to have 'true bypass' capabilities then when the unit is in 'not effecting' mode the guitar pickup signal simply passes through the unit without colouring/changing the sound in any way. Essentially, it 'bypasses' the effect. Lots of effects claim to have it, and some of these still do change the 'unaffected' sound ever so slightly.