Albumin is a class of proteins that were once thought of as core to egg white or albumen - the proteins in egg white are ovalbumin and conalbumin. Albumins are an important constituent of seeds, stored food for the embryo to use when starting life. Albumins are also found in milk and meat, being the main protein in blood plasma - this is why commercial egg-white substitutes used by confectioners may be made from blood.
Like many other proteins, albumin coagulates and hardens when heated. Ovalbumin starts to coagulate at 55 - 60oC (131 - 140oF) and is fully coagulated at 65oC (150oF), plus can also be coagulated if beaten to a foam - hence egg whites turn hard and white and beaten eggs foam to a white peak. This coagulation of its albumin proteins is why egg whites harden and whiten.