It's used to describe a young person who is exceptionally intelligent or mature for their age, often in a professional context.
For example, you might say:
* "That intern is a real Doogie, he's already publishing papers in prestigious journals."
* "My kid is such a Doogie, he's already learning calculus in elementary school."
The term is often used in a humorous or slightly ironic way, acknowledging the unusual precociousness of the person being described.