"do me a favour" is a way of asking someone to do something to help or assist you. It can be polite or not so polite, depending on the context. For example, if someone is going out on an errand, you could ask "Could you do me a favour and post this letter?". An impolite example would be "Do me a favour and shut up".
"do me a favour" is also used idiomatically to express disparagement (dis