Sync bonus: a flat +30% to the amount of points as long as you have 2+ colors matched on the grid.
Clean board bonus: After a match, nothing is on the board. You get some amount extra (a percentage bonus, 2x in Elite (or +100% if you're looking at it that way), and I'm not sure about Pro).
Basically, a large red match worth 10,000 points can be worth a LOT more depending on what else you have going for you (clean board bonus, chain bonus, sync bonus, etc.)