A mosquito uses a long tubelike appendage called a proboscis in order to bite humans and other animals and extract their blood.
The proboscis has teeth like structures that the mosquito uses to cut through the skin, and then inject saliva into the skin which acts as an anticoagulant to prevent the blood from clotting.
The mosquito then eats as much blood as it can fit into its abdominal cavity, which is up to four times as much as its own body weight.
Your mosquito bite will become enlarged and itchy due to the allergic reaction that your body has against the saliva that the mosquito has injected into your skin.
The irritation will continue until your circulatory system can clear the saliva, which usually takes several hours. In the meantime, you can use calamine lotion or hydrocortisone cream in order to reduce the itching and irritation.