The Bleeding Effect occurs when a subject begins to assimilate the memories of their ancestors. When mild, it can just mean the Animus user can then benefit from the skills to a degree. They acquire the skills that their ancestors held. This allows them to gain the balance techniques of a gymnast, the expertise of a Martial Arts master and the skills of a lifetime in a few days. The conditioning for extended usage of the skills is not there and is strictly up to the person who has gained the skills.
However, in cases of prolonged exposure, this can lead to a bleeding over of the ancestral memories onto the subject. While beneficial there are side effects that need to be strictly monitored for. They will have hallucinations of the subjects of animus sessions, seeing the ancestral memories of their forebearers. The symptoms of this effect are very similar to Multiple Personality Disorder. In essence though, it is the ancestor trying to get the user to relive all the memories of their lifetime and bring about a sense of closure.
Desmond's Eagle Vision was unleashed because of his reliving the life of Altair. This let him see the writing that Clay Kaczmarek, Subject 16, had left behind. Throughout Assassin's Creed II, Brotherhood and Revelations, Desmond benefits some from the Bleeding Effect. It was also the cause of Desmond's coma at the end of Brotherhood. The lives within were conflicting within his own. He had to finish reliving their memories to create a nexus within his mind so that everything could get sorted properly and he could regain consciousness. This negated the worst of the Bleeding Effect and stopped Desmond from losing his mind to his Ancestors.
With the successful compartmentalization of his memories and his ancestors, Desmond was one of the first to master the bleeding effect.