Often when you hear a guitar player strumming some chords and you notice some motion going on within the chord that sounds nice and interesting – frequently, what they're playing are called “suspended chords” (or sus chords)
Suspensions or suspended chords come in two varities – sus4 chords and sus2 chords. A suspended chord substitutes either the 4th or the 2nd in place of the 3rd. Ex) Csus4 = C – F – G and Csus2 = C – D – G.
If you're playing a sus4 chords, most musicians just call that it a sus chord (the sus4 is a given) and if you're playing a sus2 chord, you need to call it as such.
An aspect of sus chords many musicians aren't aware of is the fact that you can suspend many chords, not just major. Here are some examples: C7sus = C – F – G – Bflat, C6sus = C – F – G – A, C9sus = C – F – G – Bflat – D, C7sus2 = C – D – G – Bflat.
I suggest that you take every major and dominant chord you know and practice making them into both sus and sus2 chords. Also, remember you can often do two versions of each suspension by placing the 4ths and 2nds into different octaves.
Generally, suspensions are useful whenever you're playing a chord for some length of time.
Also, suspensions are frequently played withing single note, arpeggiated chords. A famous example is in the intro of the Boston song “More than a Feeling”.