The capo slider allows OnSong to adapt the chords based on capo position. This maintains the key of the song found in the transpose slider but alters the chords to work with the capo. You can capo from 0 to 11 and determine if the capo is applied by toggling the power button on the right.
By default, increasing the capo slider will modulate the chords of a song down. The reason for this is to allow the declared key of the song to be maintained. For instance, if the key of the song is C#, and a capo is applied on the first fret, then you should set the capo slider to 1. This will display the chords of the song down one half step in the key of C.
You can change how capo effects your chord chart in Settings » Display Settings » Song Formatting » Capo. You can tap on the left and right sides of the slider to adjust the capo up and down one fret.