What's the name of the move where the player swaps King and Rook/Castle in Chess? Why is this move important?
It's called castling. It's important because it gets your king out of danger (the centre is not safe), while simultaneously moving your 'tower' (also called a Castle, or a Rook) into the centre, where it is much more useful.

See this related question: Is castling still done in the openings in modern chess?