Isn't it used to take optimizations made for consoles and transfer those to PC?
Sort of. Mantle, as is speculated, will allow developers to make console-like optimizations on GNC hardware. The console APIs are different, and the interaction will be different, however, a lot of the code used may end up being reusable. How much? Well, that depends entirely on the developer I'd think.
How much performance is that actually going to translate to? Again, that depends on the developer, but also on how much overhead is actually removed. Even with removing the DX abstraction layer, there is still an abstraction layer of Mantle (at least, I imagine). How efficient that is, AMD has yet to say.
It also comes down to an ease of use for developers. I think it will end up being similar to Java and Hibernate. Object mapping from a database can be done at a more efficient level than Hibernate does, however, it will take a very specialized developer to do that. The API is incredibly easy for novices to pick up enough to work with, it isn't worth writing much of the code (and a lot of it is boilerplate code) for the minor performance gains you COULD get if you knew exactly what you were doing. I believe Mantle will end up being largely the same. The vast majority of code monkeys hired to work on these games, will stick with DX because it is easy and they can do fine with it. The studios filled with much better, more specialized developers will be able to use Mantle to create their own paths around DX and get some performance boosts.