When you move a heated iron up and down a pair of trousers it causes the trousers to fold and a resulting line is noticeable on the front of the trousers. what do you call that "line"?
That line is called a crease.
a line on cloth or paper where it has been folded or crushed:
He ironed a crease down the front of each trouser leg.
A traveler's crease is the specific crease in the front of fancy slacks. As one website says:
The crease that runs vertically down the front of most slacks – pants that aren’t chinos or denim – is there to add sharpness and sophistication to your look. This fold, also known as a traveler’s crease, helps keep your pants neat when you hang them in a garment bag as well. You’ll typically find them on work, semi-formal, or formal pants.