Why do Mormons use the term "elder" for their missionaries?

Most of the Mormon missionaries I've encountered are young men doing a couple year stint. They are typically identified as "elders", but my understanding is that this designation is only temporary during their time of service. How is the LDS use of this term similar or different than the office of elder in mainstream Protestant circles? Does their designation as elders give them any ruling authority over the church body or is their role strictly to work with non members?