LLVM's C++ standard library is libc++ and it's targeting the C++0x standard. Also separating it from libstdc++ is that it's being licensed under a BSD-style license like LLVM itself. Some of the other LLVM libc++ features beyond conforming to C++0x is fast execution, minimal memory use, faster compile times, and ABI compatibility with GCC's libstdc++ for some low-level features.
The libc++ library is being supported by Apple and at the moment this library is only supported on Mac OS X i386/x86_64, but Linux support is likely not too far out. The project page for LLVM's new C++ standard library can be found at libcxx.llvm.org. There's some tests on the mailing list showing it being much faster than libstdc++: 5 seconds versus 22 seconds.