If our skin is burned by the sun what causes the red color of the skin?
Sunburn causes damages in the skin which further triggers an immune reaction.
This immune reaction causes a dilation of the capillaries in the skin to allow a higher transport rate towards the inflammation site. This dilation and the higher blood flow in the area causes the "redness" of inflamed tissues. See the image for illustration (from here):



The delay in the appearance (for more severe cases also the swelling) is caused by the time it takes for the body to react and to develop an immune response. For further information you can look here and here.