This is the historic origin of the name, but I'm not sure it's still supposed to be an acronym. Modern ML may just be named with two arbitrary letters, as often happens when things named by acronyms grow beyond their original domain.

The "meta language" part refers to MLs original domain of writing tactics for proof assistants, where the "object language" was the language of the programs you were manipulating, and the "meta language" is the language in which you manipulate the programs. This also sort of makes sense when using ML to write a compiler (the "object language" is whatever you're compiling), but of course modern ML goes far beyond just language processing, even if it's still pretty good at it.