For a developer that doesn't know about Test-Driven Development, what problem(s) will be solved by adopting TDD?
[EDIT] Let's assume that the developer already (ab)uses a unit testing framework.
Here are three reasons that TDD might help a developer/team:
One reason to write the tests first is to have a better understanding of the actual code before you write it. To me, this is the main benefit of test driven development. When you write the test cases first, you think more critically about the corner cases. It's then easier to address them when you write the code and ensure that they're accurate.
Another reason is to actually enforce writing the tests. Often when people do unit-testing without the TDD, they have a testing framework set up, write some new code, and then quit. They think that the code already works just fine, so why write tests? It's simple enough that it won't break, right? But now you've lost the advantages of doing unit-tests in the first place (completely different discussion). Write them first, and they're already there.
Writing these tests first could mean that you don't need to launch the program in a debugging environment (slow — especially for larger projects) to test if a few small things work. Of course there's no excuse for not doing so before committing changes.
Convincing yourself or other people to write the tests first may be difficult. You may have better luck getting them to write both at the same time which may be just as beneficial.