This is a shifting of normal rhythmic stress from the strong beat to the weak beat, accenting the offbeat and playing one rhythm against another in such a way that listeners want to move, not their heads, clap hands or dance.
Syncopation is basic and continuous in Jazz and, upon it, are built very complex rhythms.
This is composing as one plays, or making up variations on old themes directly on the instrument being played rather than from written notes. Improvisation spotlights the interest and beauty of the individual performer. In Jazz, this is not limited to percussion beats alone. This is a single rhythmic phrase repeated over and over, usually as a background to the lead melody. A a riff may be used also as a melodic theme itself.