Chicken pox is caused by a virus that attacks the body and one of the ways the body defends itself against the infection is a process called inflammation.
When your skin is inflamed it makes the blood vessels open out and get red. So the skin looks red, too.
In the middle of the redness in chicken pox there is usually a little blister and that blister is loaded with the virus. That's why you're not allowed to go to school till all the blisters are broken and are dried up.