An internship is when (usually a college undergraduate) goes and works for a company who can get away with paying him a very small salary or often nothing because he hasn't graduated yet.
It's basically just working to make someone rich and getting nothing in return - the modern equivalent of slavery, except nowadays, people are actually willing.
Person A: Hey! I got an internship with yahoo this summer!
Person B: Awesome! What will your job involve?
Person A: Correcting grammatical errors, making cups of coffee.. you know the usual - they're paying me $50 bucks at the end of the six weeks.
Person B: That sounds fantastic! That'll really benefit your career in the years to come.