Examining I iii IV V
Let's translate the progression into the key of C major just for simplicity. In C major, I is the chord C major, iii is E minor, IV is F major and V is G major. You didn't really specify the timing of the chords, so I'll assume, like other answers did, that you're referring to each chord taking up an entire bar as shown below:
This progression can be viewed as a I, I, IV, V progression, which is a common progression (will be explained why it works more below). Some argue that chords in a lot of music can be broken down into either the I, IV or V chord. So where does the E minor chord fit in? It's called a chord substitute. All chords have substitutes that they can use. C major has the notes C, E and G. E minor shares most of those notes since it has E, G and B. The iii chord is a good substitute for the I chord. We can say that I and iii share the same function in this chord progression. There is another good substitution for the I chord, it's vi (ACE). For the IV chord, we can substitute with ii or vi and the V chord can be substituted with iii or vii° (but you may find vii° to be a strange one). Here are a alternate chord progressions based on this concept:
Original: I, iii, IV, V
Alternate 1: I, I, IV, V (substituted iii with I)
Alternate 2: I, iii, ii, V (substituted IV with ii)
Alternate 3: I, iii, vi, V (substituted IV with vi)
Alternate 4: I, iii, IV, iii (substituted V with iii)
Alternate 5: I, I, ii, V (in jazz, ii is more commonly used when going to V)
Alternate 6: I, vi, ii, V (very common jazz progression...see if you can figure out the subs)
This is part of the answer.
Why Does I iii IV V Work?
When we design a simple progression in certain genres of music (classical, pop, rock, etc), we have two things:
- Movement away from "home":
a) "Home" is another way of referring to the tonic. The tonic is the chord that produces the least amount of tension in a chord progression. In this case of the key of C major, the chord C major is the tonic, but if you're in a minor key like A minor, the A minor chord would be the tonic. If you're in a mode like F Lydian, F major would be the tonic.
b) In most progressions, the tonic is followed by a series of chords that add interest to the progression, but also create tension.
- Movement back to "home": This is known as a cadence. The most common cadences in traditional music theory are the V to I cadence, which may be a point of resolution for your I iii IV V progression after the V chord. Another common cadence is the IV to I cadence. If we're in a minor key, V to i is very common. Modes do not usually for the V to I trend, but they have multiple cadences for each mode as well, depending on the mode.
In conclusion, when creating a chord progression, decide on a key, start with the tonic of that key, add chords that move away from the tonic and then make your way back to the tonic by the end of the phrase and you'll be making great chord progressions in no time.