Hello Free Adam,
Thanks for the question.
The Apple Thunderbolt Display requires Thunderbolt-enabled Macs, including the current generations of MacBook Air, MacBook Pro, Mac mini, and iMac. Unfortunately, your MacBook does not have a thunderbolt port, so it would not be compatible.
However, depending on what model MacBook you have, it may be compatible with the Apple LED Cinema Display, which utilizes Mini DisplayPort input. This was included with the MacBook (13-inch, Late 2009)
If you need help identifying if you have the Early, Mid, or Late 2009 model, see this article: