LuaTeX is an extension of TeX which integrates Lua (a scripting language) into TeX. LuaTeX is an extension of pdfTeX, which means that both DVI and PDF output are possible. LuaTeX makes it possible to access the internals of the TeX process 'as they happen', allowing effects that are difficult to achieve otherwise. It is also Unicode-capable and can use OpenType and TrueType fonts.
Use this tag if your question is about LuaTeX or LuaLaTeX specific problems and is not related to general (La)TeX issues. ConTeXt Mark IV uses LuaTeX as its engine: if the question is about ConTeXt and LuaTeX, use context-mkiv instead.