The most common use for a capo is to increase the pitch of the open strings. Whichever fret you attach the capo to effectively functions as the open string. This means that the open, unfretted notes are higher than usual, permitting you to play open chords higher up the fretboard. For example, with the capo on fret three, your first finger goes on fret four, rather than fret one, to make an E major chord. You treat the capo as if it were the nut. This application is convenient for singers who want to alter the key of a song to a higher one without transposing the chords or retuning the guitar.
The gap between frets on a guitar decreases the further up the fretboard you go. For beginners, it's easier to practice chords on smaller frets. By placing a capo on the guitar and down-tuning the guitar to compensate for the pitch-increase, a beginner can make fret two or three function as if it was fret zero, or the open string.
Neck relief is the amount of bow in the neck, in relation to the body of the guitar. One way of measuring relief is to fit a capo to fret one and another capo to fret 12. Observe the angle of the string between these two points. If the string slopes upward, the neck is forward-bowed. If it slopes down, the neck is back-bowed.
By fitting a capo just behind the nut of the guitar, you don't alter the pitch of strings; you merely limit the amount by which they can resonate. This technique is useful when trying to record an acoustic guitar, as it cuts out unwanted string noise and vibrations. The drawback of this technique is that it can cause the strings to go out of tune quicker than they would without a capo.
