used after the negative stem of a verb to mean 'without doing ...' or 'instead of doing ...' (e.g., 'without doing A, do B').
朝ごはんを食べないで学校へ行った。
I went to school without eating breakfast.
宿題をやらないで遊びに行くのはよくない。
Going out to play without doing your homework isn't good.
傘を持って行かないで後で濡れてしまった。
I didn't bring an umbrella and got wet later.
used sentence-finally as an informal prohibition or request not to do something (e.g. 'don't come', 'don't touch').
そんなことは言わないで。
Don't say that.
ここに車を止めないでください。
Please don't park your car here.