At it's most basic - a May system is simply internal micing. The mics are mounted inside the drums for conveniance and consistantcy. Nornally, it requires cutting a small hole in the drum shells for the XLR jack. You can pick and choose various mic combinations to be mounted in the drums.
I've used a May system - but I am not a fan. While is is very conveniant and it does eliminate the need for mic stand, clips, etc. - it can create certian EQ problems. I found that the drums had too much low end and had to be EQ'd (often a lot) at the board.
Since the mics are inside the drums you pick up a lot of the internal resonance, in addition to the attack. Naturally an external mic placed at the batter head picks up mostly attack and then room ambience and overhead/area mics poick up the resonance.
For soom people a May system could possibly make since in a live setting, however, as I said, I was not overly satisfied - but I would never consider this for recording.