is an expression that is used to politely ask someone ‘not’ to do something. It is a combination of the casual negative form of a verb, the で
particle, and ください (the conjunctive form of くださる).
ください is classified as 尊敬語（そんけいご）, a type of polite speech that is used to refer to the actions of other people. The ください form of くださる is used almost exclusively for making requests. くださる is the polite (sonkeigo) equivalent of くれる
In friendly conversation, ください may be omitted from this expression, and the で
form itself can be used as a very casual way of saying ‘please don’t do (A)’.
Because that's my older brother's, please don't eat it.
Because I'm going to call you later, please don't sleep.
Although ください is the polite form of くれる, ください is considered the base form of this phrase, and ないでくれ (the conjunctive form of くれる) would be considered far too casual in most situations.