The synthetic a priori is a term coined by [[Kant]] describing a type of [[judgment]]. This was his breakthrough thought.
A synthetic a priori judgment is a judgment presupposed by the possibility of experience. For Kant, for example, causality was a synthetic a priori judgment. If I throw a ball into the air, do I need to have done so to guess what will happen? Kant would say no, whereas [[David Hume]] would say yes.