Suspended chords can really spice up triads and seventh chords. Sometimes they are played by themselves and sometimes they precede the regular triad or seventh chord they're "suspending".
So what does "suspend" really mean?
Well one of the most important notes in major and dominant 7 chords is the third. It's important because the third is the "leading tone". For example, if you have a G7, which is often followed by a C chord, the third of G7 is a B and "leads" you up a half step to the next chord.
Now when you suspend a chord you are really raising the 3rd up to the 4th degree. Hence the chord symbol, sus4, though you may see just the 4 as well (as in F#4). So a C triad is C, E and G while a Csus4 is C, F and G. You can also see it in a seventh chord with the chord symbol, sus7. For example, Csus7 is C,F,G and Bb.
Now occasionally you will see a sus chord that uses the second note instead of the fourth to replace the third. These are called sus2 chords or just 2 (as in F#2). For example, Csus2 is C, D and G. These are not to be confused with add2 chords which include the second degree along with the third degree, Cadd2 is C, D, E and G.
Suspended chords often "resolve" to the major triad they're suspending. This happens a lot in cadences, especially in traditional classical music.
Also whenever you see a major or dominant 7 chord, you can first play a sus chord and then resolve it back to the major or dominant 7 chord. You can even go back and forth multiple times.
I'll often "suspend" the fifth up to the sixth in addition to the fourth. For example, when I play a C chord I'll play the C, E and G and then, C, F and A and then back to the C, E and G. It sounds really bluesy and soulful.
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Chord Inversions and Voice Leading