Chords prefaced by the number 2 are not standard chords and "2" is not a standard chord symbol, but appears fairly often in tablature and chord charts for modern music of all genres but particularly in Christian and country music. Taking the chord of C as an example, a C2 chord means that you can play a variation on the C major chord. When you come across a C2 written on a set of sheet music, its possible to play a Cadd9, a Csus2, or even a plain C chord. Which you choose is up to you and is dependant on the one you think fits best with the piece you are playing.
For each chord, the significance of "2" is more or less the same. For the chord of A for example, "2" is often used to represent a possible choice between the chords Aadd2/Aadd9 or Asus2/Aadd9 depending on what sounds best and how much you like to experiment.
In practice, "2" chords can make playing more flexible. Unless you want to sound exactly like a recording or the original of a song, "2" chords give the player a certain amount of flexibility when deciding how to play the chord.