Basically, the idea is to move the data required to verify the validity of a transaction into a new "witness" data structure and out of the transaction itself (hence "segregated witness"). This makes transactions (and thus blocks) slightly smaller, among some other benefits.

Since butters are deathly afraid of changing the sacred rules of the BitCoin, SegWit is implemented as a "soft fork" by loosely bolting this new scheme onto the old protocol without directly breaking anything, supposedly maintaining backwards compatibility. However, this is mostly a sham since old clients do not know about the witness data and can't validate transactions anymore (they'll assume everyone can redeem any SegWit transaction), and it makes the implementation incredibly complicated and presumably error prone.