Extrinsic motivation is motivation that requires a source external to the agent who is motivated. I had to put that a little carefully, I was initially going to write something like "motivation that does not originate within the agent...", but that's debatable, isn't it? One could argue that even external motivation requires an internal value judgement.
Safer instead to say that external motivation means motivation to gain a reward from someone or something outside the self, or avoid punishment from someone or something outside the self. Hmm, looks like the whole notion of external motivation might supervene on a self/not self distinction being meaningful.