The dissolution means that the blood is breaking down.

The word “dissolution” means that something is dissolving.  The word is used to describe the dissolving of the victims' blood when the Red Death takes them. 

There were sharp pains, and sudden dizziness, and then profuse bleeding at the pores, with dissolution.  The scarlet stains upon the body and especially upon the face of the victim, were the pest ban which shut him out from the aid and from the sympathy of his fellow-men.

As you can see, the blood dissolving from the pores of the victim causes red stains.  This is because a person’s blood literally weakens.  The red stains mark the victim, and make him a pariah.

The disease is a terrible one.  Its description is similar to the Bubonic Plague, or “Black Death” that decimated Europe in the middle ages. In this case, the “Red Death” gets its name from the blood that leaks out of victims’ pores.

A disease this strong kills its victims fast, and is very contagious.  This is why it kills half of the population of Prince Prospero’s kingdom.

When his dominions were half depopulated, he summoned to his presence a thousand hale and light-hearted friends from among the knights and dames of his court, and with these retired to the deep seclusion of one of his castellated abbeys.

Despite the safe haven of his castle, Prospero and his courtiers cannot escape the disease.  Death still finds them, and even then Prospero deludes himself into believing he can fight it.  Ultimately, not only does Prospero fall but so do all of his constituents.  No one can escape the Red Death.  Prospero would have been better off staying with his people and trying to help them in whatever way he could.

Metaphorically, the Red Death represents threats that a leader faces.  Prospero reacts in a deluded and selfish manner, and puts his own life and comfort ahead of his people.  The people inside the abbey are living out a kind of fantasy, and one that cannot possibly last.