MECE is an acronym that stand for Mutually Exclusive, Collectively Exhaustive. It is pronounced like "me see".
About
This is most commonly used (in my experience) when trying to come up with terminology that describe something. The thing being described is thought to be capable of being broken down into chunks that can be named. The idea is that you have "good terminology" when you have a word for each chunk that doesn't overlap with other words (mutually exclusive) and also that each chunk has a word for it (collectively exhaustive), aka, there are no unnamed chunks.
This is similar to the concept of a bijection in mathematics, in that mutually exclusive represents a 1-to-1 mapping, and collectively exhaustive represents an onto mapping. The difference is that a mapping goes from element to element, while MECE is mapping words onto sets of entities within the space.