The eggs are laid into water...like he said standing water. Even a puddle that stands too long. They hatch into what we call mosquito larvae. They almost look like tiny shrimp. They appear to swim by curling their head to their tails, but if disturbed they are able to make a bee-line for the bottom. They bite too!
Mosquitoes breed in standing water, like swamps or ponds. Or if you have a poor neighbor they can live in poorly maintained swimming pools :( I think they are born as little bugs before they become mosquitoes but I'm not sure.