Yiddish word, borrowed into English slang, for "backside, ass, arse, behind..." well, you know what I mean. Where you sit. The permanent vertical smile. Sometimes spelled "tuckas" or other variants, depending on transliteration and pronunciation of the speaker.

It's from the Hebrew word "tachat," meaning "under, underneath." It also refers to the butt. The usual Yiddish pronunciation-changes happened, shifting the stress to the first syllable, exaggerating the backness of the vowel, reducing the second syllable's vowel, and the s pronunciation for the "soft" t at the end. Similar workings happened to tzuris, shabbos, etc.

I suspect that softening the consonant led to the version "tush," but I'm not sure about that.