A document can be viewed as an object with a set of pointers to the words it contains.
The inverse of that, was a word object, with a list of pointers to the documents it is found it. This was referred to an an inverted DOCUMENT index. This is what people would normally just call an index.
At some point, people dropped the "DOCUMENT" part, and started just calling it an "inverted index". This makes no sense, grammatically, as it's the document that is inverted, not the index, but it is what it is.
It's a fun project, because I have to do hardware for it, and that's outside of my current skill set.