Like others have said, it's a prepaid card that allows you to travel on the tube/bus. You just swipe it at the barriers and voila! It lets you through.
You can get different types: standard and student Oyster Cards.
If you plan on doing a lot of weeking travelling across London, getting a Student card would be a good idea as you get a discounted fare. However, to get this fare, you need to by a weekly travel card so it would only be worth it if you have to make regular travel to lectures/your part time job etc...
On a standard Oyster card you can either buy a weekly travel card or you can Pay as You Go allowing you to put on as much credit as you want.
If you have a student railcard you can link it to your standard Oyster to get a reduced fare on journies.