, it allows for a reduced transaction size, and therefore also reduced fee and increased transaction speed. To put it as simple as it gets.
sometimes people oversimplify some concepts to a point where it becomes wrong!
in this case SegWit does NOT reduce transaction size or transaction speed.
in fact SegWit transaction size is a tiny bit bigger. what it does is that it increases capacity by changing the way transactions are stored in the blockchain. it moves the "witness" which is the signature to another place which helps with backward compatibility while increasing the capacity of blocks.
you pay a lower fee on a SegWit tx not because the tx is smaller but because of this change and the way virtual size is calculated.
as for transaction speed, it is decided based on time between blocks which is a fixed time (10 min on average) and that is not changing with SegWit.