Natch is a short, jokey way to say naturally — “of course; just as you’d expect; that was never in doubt.” It is casual American slang, a bit old-fashioned now: the sort of thing you might hear in an old film, or from someone being playfully retro. “He forgot his keys, natch.” It is a wink, not a careful explanation. You would not write it in school work, a job letter, or news, and many younger speakers have never used it at all. There is an unrelated older noun natch for an animal’s rump; that is not this word.