Arpeggio
An arpeggio is a chord played one note at a time instead of all at once. The notes are exactly the chord's notes - root, third, fifth and any extensions - just spread out in sequence rather than sounded together. A chord played as a block is harmony; the same chord rolled out note by note is an arpeggio.
Arpeggios sit somewhere between chords and scales. A scale gives you a set of notes that work over a whole key; an arpeggio gives you the notes that fit one specific chord. That makes them especially handy when you improvise a melody over a progression: you can follow the chords closely by drawing your notes from each chord's arpeggio, and switch arpeggios as the chords change.
Why they sound good
Because an arpeggio is built from chord tones, it lines up with the harmony underneath, which is why melodies and solos that lean on arpeggios tend to sound melodic and intentional rather than generic. Arpeggios are also a way to imply a chord progression with a single line - pick out the notes of each chord in turn and it sounds almost as though the chords themselves are being played. And spreading the notes out means you can use rich or clashing chords that might sound harsh struck all together.