Intrinsic motivation is the desire to do something for the inherent satisfaction of completing the task. This type of motivation is largely internal and can be less affected by external factors, though certain external pressures may push one to complete the task out of a sense of obligation rather than satisfaction.
For example, an individual may have a goal of writing a book and be motivated to complete it because it is a creative challenge they've set for themselves. While they may be pressured to finish by an external deadline, they are still motivated to write because they find joy and satisfaction in completing the task.