There are many different kinds of mosquitoes. They can carry viruses, parasites, and other things that can cause diseases in people and animals. It's only the female mosquito that bites and sucks blood. They need the protein in the blood to mature their eggs. Blood is not a food for mosquitoes. They eat plant nectar.
When a mosquito bites you, it pushes a needle-like mouth part into your skin. This mouth part has two tubes. Through one tube, it injects saliva that has an enzyme that stops blood from clotting. Through the other tube, it sucks your blood. It's the saliva that causes the local allergic reaction that you get from a mosquito bite.
A mosquito bite may cause redness, swelling, and itching. Some people are more sensitive to mosquito bites than others. They may feel dizzy and weak.