In my opinion there are two major benefits you can get from a good understanding of the STL.
1 - The most obvious one is that you improve your C++ abilities. You can do pretty amazing things combining all STL capabilities like containers, algorithms, iterators and function objects. Most fundamental algorithms and data structures are there.
2 - You can learn from its design. In particular, you get a feel on the power of
generic programming, which is the development paradigm of the STL. (If you don't know yet, the STL is not constructed on a traditional object oriented paradigm.) You'll have a great example of how to build reusable and extensible software libraries.