When you play individual notes of a chord one at a time instead of as a unit, it is called "arpeggiation". So an arpeggio is simply a broken chord -- a chord broken up into it's respective individual notes.
You often hear beginners play simple arpeggios, such as the C chord repeated over and over up the keyboard or back down. But arpeggios can also be complex; for example, you can arpeggiate any extended chord such as a 9th or 11th or 13th or any alteration. And you don't have to go straight up the keyboard -- you can hesitate in any octave, then continue, or head back down and then up, or change chords in mid-stream -- there are lots of variations.
For an example of arpeggiation, you might want to take a look at the short video on tremelo-fired runs. It is an example of one type of arpeggio, yet beginning with a tremolo.
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