It developed primarily for use as an embedded language, so the Lua authors have kept the core very small. It's easy to use it with C, and to extend the core with libraries written in C or Lua. Many things that other languages require in the core can just be loaded as libraries. This means that (much like Scheme) it makes for a clean foundation for interesting CS projects -- LPEG (http://www.inf.puc-rio.br/~roberto/lpeg/lpeg.html) is a novel parsing/pattern matching system, there's a new library to add Erlang-style concurrency (http://concurrentlua.luaforge.net/), LuaJIT (http://luajit.org/) is a cutting edge JIT compiler, etc.
It's trivially portable to anywhere C is used, and is quite fast. It's also distributed under a BSD license, if your company wants to use their own fork internally (it's ~500k of source). You can also deliver executable files with byte-compiled Lua embedded in them.
Stylistically, it's probably closest to Python, but with more Scheme influence (tail-call optimization, coroutines, non-crippled "lambdas", etc.). It's idiomatic to make heavy use of tables, which are very similar to Python dictionaries.
The standard intro is _Programming in Lua_ (http://www.inf.puc-rio.br/~roberto/pil2/). The first version (covering Lua 5.0) of the book is free online, but there were some significant changes to the language with 5.1, particularly the module system.
It has some downsides as a Language (the community, while nice, is rather small, so sometimes documentation is sparse or scattered; it's generally assumed you're already using C or C++, so the standard libraries have gaps when using Lua on its own; the module system is still maturing (LuaRocks (http://luarocks.luaforge.net/rocks/) is an attempt to fix this); etc.), but picking any particular language always involves trade-offs. I've been quite pleased with it.
(Also, MIT license, not BSD.)