The "blue" part of the word stems from the fact that U of M's school colors are maize and blue. Also, its fans will cheer, "Go Blue" to show support for their team. The "blood" part is meant to define the emotion of passion that all people have to some extent. As a compound word its intent is to imply that a blueblood's passions are somehow tainted and/or inappropriate. Transversely, Ohio State's school colors are scarlett and gray. As most Ohioans that watch collegiate football are supporters of the Ohio State Buckeyes, and as Michigan is Ohio State's archrival, the term is intended to express a negative, ostrasizing connotation.
It also refers to old money families: families that have been aristocrats for many generations.
The blue blood of the elite could not be tainted by the blood of commoners, lest the whole line be polluted (disregarding the risks of inbreeding).
Now it generally refers to people from old money: families who have been wealthy aristocrats for generations on generations.