A simplistic way to describe it is when you push the clutch in while activated, it puts a tempearary rev limiter during shifts, making one less thing for you to do wrong. Computers > humans.
Since you edit yours, I will edit mine.
It is bad to just hold the gas and shift without it for a few reasons. One, if you do that, your going to have your revs shoot up ever shift, then shoot back down when your transmission slows it down. This results in tremendus shock on both your engine and your transmission.