It's an idiom, the correct form of it is "Мели́, Еме́ля, твоя́ неде́ля". It's colloquial, it expresses disbelief in what another person says while being unable to stop or influence the speaker in a way.
Еме́ля is short for the name Емелья́н, the whole phrase can be translated as "Grind, Yemelyan, it's your week." It originated in the times when in big peasant families each member did just one kind of household work, and each week the work one did changed. Grinding grain on a hand-powered grinding wheel was difficult work, so the phrase was jokingly said to someone who was lazy. In addition, моло́ть языко́м, 'to grind with one's tongue', or simply моло́ть is another idiom meaning 'to say nonsense', like here:
"Что ты ме́лешь?" - 'What nonsense you are saying!'
So the general idea of Мели́, Еме́ля, твоя́ неде́ля is something like "stop saying nonsense and do some work."