What is Clang?
Clang is an "LLVM native" C/C++/Objective-C compiler, which aims to deliver amazingly fast compiles, extremely useful error and warning messages and provides a platform for building great source level tools. The Clang Static Analyzer is a tool that automatically finds bugs in your code, and is a great example of the sort of tool that can be built using the Clang frontend as a library to parse C/C++ code.
What is LLVM?
The LLVM Core libraries provide a modern source- and target-independent optimizer, along with code generation support for many popular CPUs (as well as some less common ones!) These libraries are built around a well specified code representation known as the LLVM intermediate representation ("LLVM IR"). The LLVM Core libraries are well documented, and it is particularly easy to invent your own language (or port an existing compiler) to use LLVM as an optimizer and code generator.