He was talking about a technique of throwing a jab like Kostya Tszue
Exactly, though we lean forward far less.
Actually, I was taught to do jabs both ways - with leaning forward and being in a balanced stance (as greynotsoold wrote) but in sparrings we always opt for jabs like Kostya Tszue showed.
That's because my trainer told us that we should keep our upper body moving back and forward all the time. It was drummed into us and our sparring strategy was built on it.

Thanks for the tips, if i have more questions I'll come back again