Only female mosquitoes bite. They need the proteins found in blood to nourish their eggs. They find their victims by the carbon dioxide generated when we breath, body heat, and even body odors which can make them attracted to certain people as opposed to others.
When mosquitoes bite, they use a syringe like appendage called a proboscis. When they use this syringe, they inject some of their own saliva which contains an anticoagulant as well as various proteins. This prevents the blood from clotting which allows it to freely flow into the mosquito. When your body comes across the proteins the mosquito deposited it releases histamines, which are a compound that white blood cells use to get to the area. This causes inflammation and swelling which sends a signal to the nerves around the bite telling your body there is an itch.
It is possible after constant exposures to develop a resistance to this effect but each type of mosquito has its own proteins which means a different species of mosquito will cause you to itch all over again.
In order to prevent this, try and eliminate any standing water that has accumulated in flowerpots, low spots, and check that your gutters are also free of debris and draining properly. Eliminating their breeding spots will significantly reduce their population.