What is the function of red blood cells?

Erythrocytes, or red blood cells, are the primary carriers of oxygen to the cells and tissues of the body. 
The biconcave shape of the erythrocyte is an adaptation for maximizing the surface area across which oxygen is exchanged for carbon dioxide. Its shape and flexible plasma membrane allow the erythrocyte to penetrate the smallest of capillaries.
Red blood cells make up almost 45 percent of the blood volume. 
Their primary function is to carry oxygen from the lungs to every cell in the body. Red blood cells are composed predominantly of a protein and iron compound, called hemoglobin, that captures oxygen molecules as the blood moves through the lungs, giving blood its red color.
As blood passes through body tissues, hemoglobin then releases the oxygen to cells throughout the body. Red blood cells are so packed with hemoglobin that they lack many components, including a nucleus, found in other cells.
The membrane, or outer layer, of the red blood cell is flexible, like a soap bubble, and is able to bend in many directions without breaking. This is important because the red blood cells must be able to pass through the tiniest blood vessels, the capillaries, to deliver oxygen wherever it is needed.
The capillaries are so narrow that the red blood cells, normally shaped like a disk with a concave top and bottom, must bend and twist to maneuver single file through them.