The add2 chord is very similar to the add9 chord; the notes are in fact the same, but the difference is that the add2 and the add9 note belong to different octaves. You probably know that a common major chord includes the first, the third and the fifth note in its scale. By adding the second note, you get an add2 chord.
So if we take C major as an example, what happen is what C, E and G changes to C, D, E and G.
Add2 are in general not often used in songs. Cadd2 is an exception and is one chord you should try to memorize. Also notice that sometimes are the exactly same fingerings use for add9 chords. For the most times, the ambition is to present two different chords with the correct order of notes, but you will not make a big error if you use an Add2 chord instead of Add9 and vice versa.
Sometimes these chords are just referred to with the number two in the chord name, as C2, D2, E2 and so on.
Chord progressions with add9 chord
Some examples of progressions using add2 chords:
C - Cadd2 – Fadd2
Aadd2 – D6 – Emaj7