A laser printer works like a photo copier and has a "toner" (black dust) that is fired on to the paper and sticks there.
Ink jets have small cartridges containing a liquid ink that is squirted onto the paper (different companies do have slightly different technologies).
Ink jet printers tend to be cheap to buy (particularly for colour) but expensive to run. Sometime one cartridge can cost the same as the whole printer.
Often companies sell their printers at a loss, but make their money on the ink. Which is why you see cheap ink jet printers in Tesco, Sainsburys, W H Smiths etc
Lasers tend to be cheaper to run (cost per page) but the printers are more expensive to buy, particularly for color. Mind you replacement toners are expensive.
I bought a Samsung B/W laser a few years ago for about �35 (the model was being replaced) and it did me loads of pages, but a new toner cartridge will cost me over �50.
I have the cheap laser printer (Samsung) that I use for black and white printing, but an ink jet for colour.