My friend tells me a suspended chord means you hold down the sustain pedal but that doesn't sound right... Can someone help?
Your friend seems to be confusing 'suspend' and 'sustain'.
Here's more than you probably want to know about suspensions.
Consider an F major chord followed by a C major chord. Let's root them both on C. So we've got C, F, A followed by C, E, G. The F falls to E, the A falls to G.
Now, suppose we hang on to the F a bit longer, delaying its move to E. We call this a 'suspension'. When it eventually does fall to E, that's a 'resolution'.
If we're thinking in chord symbols, that's F, C(sus4), C. Or, as a suspended 4th is the most common suspension, just F, Csus, C.
The traditional rule was that the suspended note (F in this case) had to be 'prepared' in the preceding chord. Then the idea of an 'unprepared suspension' came along. And now we even commonly use 'unresolved suspensions', where a Csus chord can come out of nowhere and not be required to resolve to C.
"Suspended chord" means the same thing on piano that it means elsewhere: it is a chord whose components are derived from the common-practice harmony technique of suspension, in which a chord tone from the previous chord is held over for a while. For example, there might be three chords, F major, G major, C major. When the chord changes to G major, the part that had C in the F major chord doesn't move to B right away but instead stays on the C for a beat, moving to the B on the next beat. Since the C and B are a fourth and a third above G, this is called a 4-3 suspension.
More recently, 100 years ago or so, it became common to provide chords with popular sheet music for use with guitar, ukulele, or similar instruments. This created a tendency for the suspension to be viewed in isolation rather than as the first part of a musical gesture containing one note. The chords for this example would be given as
F Gsus4 G C or even just
F Gsus G C.
A suspended chord, therefore, is typically a chord in which the fourth substitutes for the third. That is, it contains the root, the fourth, and the fifth. Variations are possible, though; there can be a seventh (
G7sus4), and I've heard tell of
sus2 chords as well, though this notation does not seem to be standardized (see, for example, the discussion at Sus2 doesn't exist?).
As Tim notes in his answer, people sometimes misapprehend the "sus" in chord symbols to mean "sustained" rather than "suspended." As Laurence Payne notes in his answer, your friend has also confused "suspend" and "sustain," but in this case your friend has made the opposite mistake by misunderstanding the piano's sustain pedal as a suspend pedal.
A suspended chord is one which loses its 3rd, and has a P4 played instead.(Sus 4).
Often, that 3rd is lost in favour of a 2nd, which then re-names the chord 'suspended' (sus2). In reality, though, that chord should be named a retardation -(ret 2).
The suspended note sometimes is what's left of the previous harmony, but doesn't necessarily have to be. There are many times when the sus4 chord is used with no reference to the previous chord. Likewise, resolution isn't always given - though it often is the case. The general idea is that suspension gives that feeling of dissonance, which we expect to be resolved soon, and usually we reach our expectations. But dissonance may continue for longer so not get resolved by that P4 moving to 3 sooner.
With just 'sus' to go on, that's not the first time someone's thought sus(tain). Wrong!