Yes, the laminator melts the toner and makes it stick to the board. For a while I would just iron it on but that can be very tricky to do (hand pressure, etc).
I use a LaserJet 1200 which prints very nice thick toner traces.
My laminator is just a cheap one from walmart that I modified to run at a higher temperature. Even at the higher temperature I have to run the board through it 5 or 6 times (at different angles) to make sure all the toner gets stuck to the board. Pre-heating the board would probably make it require less passes but it works well enough without that. Higher-end laminators work better but of course cost a lot.
For printing I use glossy magazine paper (just pages torn out of old magazines) because it's very thin and falls apart/dissolves easily in soapy water leaving just the toner on the board. Some printers will jam when printing on this stuff but the LJ1200 works no problem.