LLVM is a compiler toolkit, used by, for example, Clang for C/C++/Objective-C, Rust, and various libraries like Mesa.

How did you find the demo page, and why did you expect it to be more useful than the front page at explaining what LLVM is?

The llvm.org front page already has "The LLVM Compiler Infrastructure Project" as its title and the first sentence of the body text is "The LLVM Project is a collection of modular and reusable compiler and toolchain technologies."

llvm is the "back-end" of a compiler turned into a reusable library, where the front-end of a compiler is what parses and understands a specific language (clang or rust being examples of primarly front-end things that leverage llvm).

if you make use of llvm, you "simply" have to parse your chosen language and hand off some intermediate form bits to llvm to create compiled binaries.