Blood that is found in an egg may not be eaten. In the times of the Gemara, such blood was usually an indication that a new embryo was forming and it is forbidden to eat an embryo. This halacha is found in Yoreh Deah siman 66. The Rema in seif 3 writes that the custom is to throw out any egg that blood is found inside of it.
But what about an egg that could not have been fertilized? Such an egg may be eaten as the Shulchan Aruch writes in seif 7 after the blood has been removed. The Gra explains that eating this blood is an issur D’Rabanan.
Therefore it would seem that a person who, following the custom of practiced by all Jewish people (Aruch Hashulchan, 32), checked eggs before using them and found a blood spot, could throw out the blood spot and eat the rest of the egg. The reason is that now-a-days there are no roosters at the egg farms and the blood found in the egg cannot be an indications of the egg being fertilized.
Indeed, Rav Moshe in Igros Moshe (Yoreh Deah I, 36) wrote that according to the letter of the law a person who finds a blood spot in an egg could simply remove the spot and enjoy the rest of the egg. However, Rav Moshe concludes that practically a person should throw out the entire egg. Because at times fertilized eggs are mixed with non-fertilized ones and they are so cheap, one should be stringent and discard the entire egg. This is also brought in the name of Rav Elyashiv.
Rav Moshe wrote this in 1957. Some people want to argue that now-a-days, Rav Moshe would be lenient. This is the position of the Yabiya Omer III Yoreh Deah siman beis.