Showing Serbian muscles is when you're trying look like a tough guy while in fact you're very week. Your muscles are those of somebody bigger than yourself but which you pretend as if you had them.
The saying comes from Serbia being in conflict with all other countries and peoples, pretending that Russia will help them out of any problem situation.
Peter: Oh, watch out that guy! He looks dangerous!
James: Don't worry, he's only showing his Serbian muscles.