These two words are some serious fundamental Yiddish right here, yessiree. They refer to craziness, or someone that is crazy, in a “you-must-be-out-of-your-mind” sense. Can also imply you’re obsessed with something or other, or you have some sort of irrational bugbear or like that.
There is often some confusion as to which word to use. Generally, you want to go with meshuggeh as an adverb, and meshuggeneh as an adjective or noun.
“What, David, that meshuggeneh? Eh, I don’t talk to him so much these days. He just keeps getting more and more meshuggeh.”