The point of a capo is, of course, to be able to perform a song in a different key while using the same fingerings and chord formations you'd use in an open position. This enables performers to stick to positions they're more comfortable with and to enjoy all the benefits — including ringing, open strings — high up on the neck.
Capos also facilitate or create alternate chord voicings and help performers accentuate certain melody lines in a song. Of course, the higher up the neck you go with a capo, the more you change the voicing of the guitar — to the point that you can even imitate a mandolin, as demonstrated by music editor Jimmy Brown (our own "Capo Crusader") in the upcoming May 2014 issue of Guitar World (which you can check out here).
Former Eagle Don Felder says it best in the top video below, which he created for Guitar World in 2012:
"When I originally wrote ['Hotel California'], it was in the key of E minor, which is a really great guitar key to play in and write in. We recorded the whole track in E minor, and then Don Henley went out and tried singing it ... and it was way too high for him ... . So I took a guitar, went out in the studio and said, 'OK, let's move it down to D minor.' Still too high ... C minor, a little bit too high; A minor; no, that's too low. It wound up being in the key of B minor, which is on the seventh fret."