At first I was confused because the pitch seemed to be mainly about writing fast code with Lua. If that's what they're going for, then a comparison with LuaJIT is sorely missing.

But it appears that what they're actually pitching is a simple and flexible code generation environment. It's a way to generate statically-typed code at runtime that targets LLVM but looks nicer than this: http://llvm.org/releases/2.6/docs/tutorial/JITTutorial2.html (C++ code that conjures up LLVM SSA IR directly). You could almost think of this as a high-level API for LLVM code generation and execution that is exceptionally well-integrated into Lua.

For example, in their example where they create a Terra function from a BF program, the equivalent in plain Lua would be to compile the BF program into a Lua program (represented as a big string), load it into the interpreter, and then let LuaJIT JIT it. But with Terra, you can represent the code you're generating symbolically with the "quote" construct instead of having to compile it to a big string. Of course you could just writer a BF interpreter in Lua directly, but if you compile it instead you'll get better performance because you won't pay an interpreter overhead and the optimizer can analyze the program flow to look for optimization opportunities.

[EDIT: removed incorrect criticism about the BF codegen being incomplete]

It's an interesting approach and I look forward to learning more about it.