People sometimes shorten "capodaster" to "capo", and the humorous reference to it as a clamp isn't too far off. It works a bit like a clamp, pressing down on the strings behind a chosen fret, basically turning that fret into a new starting point for the strings. This shortens their vibrating length, which makes them sound higher.
Functionally, a capo is like a replacement for your index finger and thumb when playing barre chords. You place the rubberized side of its top arm parallel to a fret and between two frets on the fretboard. The bottom arm gives support against the neck.
And for some geeky insight, a brief look into the history books: The first capo for the guitar was reportedly built in the 17th century and was made from a piece of bent brass. The term "capo tasto" (and its playing technique) was first used in Giovanni Battista Doni's (1593-1647) work "Annotazioni sopra il compendio."