I'm not a native speaker (I've just started learning the language), but, according to the introductory lesson attached to this unit, the "me-" prefix makes a verb explicitly transitive. For example, "saya makan" = "I am eating" (no direct object), but "saya memakan ikan" = "I am eating a fish" (fish = the direct object). Apparently the "me-" is often optional, and makes the sentence sound a bit formal. I think this is the case...I'm not positive.
This is something that has given me endless trouble since I started learning Indonesian. My sense is that native speakers tend to use -nya quite liberally to mean "the." The problem is that in formal writing, -nya is used very sparingly (and only to signify possession, I believe).