I think they made it up a while ago as an alternative to calling them "normal". That means calling ourselves abnormal, which is true statistically but has so many bad connotations that nobody even wants to be associated with it. Or maybe it's because "normal" has so many good connotations that the opposite has to be bad. Either way, I guess inventing our own word must have been a way to remove the connotations. Too bad nowadays "neurotypical" is getting slight negative connotations because of all the people complaining about getting prejudice from NTs. Of course, that's not logical because autistic people can be prejudiced, too; but I guess there are people who have been kicked down long enough that they're angry enough that they're not thinking too hard about how they're using words.
You may also hear the word "neurodiverse". That's a reference to people with atypical brains, stuff like epilepsy, ADHD, bipolar, savant syndrome, dyslexia, traumatic brain injury, giftedness, mental retardation, synesthesia... etc. It's not strictly a word for brain-based disability because it also includes things that are simply significant differences that don't cause impairment (but do have the usual sociocultural impact that any difference does).