The link provided from Secret Slave above gives a good explanation.
It is the oxygen carrying component of RBCs. Oxygen binds to hemoglobin with high affinity in an oxygen-rich environment and leaves hemoglobin in an environment where there is not enough oxygen.
You see whole blood consists of different components. One of these components has H20 (water) in it. Are you going to deprive yourself of water in an operation because it is a component of the blood cells? That is the rationale behind the acceptance of the various components