Intrinsic motivation means that you are motivated by an inner feeling, a desire to do something well because you enjoy it and feel good about it. For example:
I enjoy running and swimming so I go running and swimming.
Extrinsic motivation means that your motivation is determined by an external factor rather than the desire or feeling of enjoying the activity. Example:
Someone who is motivated only because of the perks, promotions and fame that will result from success.
Of course there can be some degree of both extrinsic and intrinsic motivation at the same time. You can work and get paid for it, and also enjoy doing the activity.
For the language learner I believe extrinsic motivation alone is not enough. The student who is unable to enjoy the process of learning usually encounters great obstacles. It is the student who has a real feeling of enjoying the process of learning because of curiosity and playfulness that gives the best and fastest results.