"To give it a rest" is used to tell somebody to stop talking about something because they are annoying you. "To give something a rest" means to stop doing something for a while.

I say this to my students who constantly complain about how much homework all their teachers give them because it interferes with their social life.

Resting is the period of time in which you relax, do not do anything active, or sleep. The same is valid to things. You can also use “stop doing it for a while”, as Ayim said.

Stop doing something. http://idioms.thefreedictionary.com/Give+it+a+rest!