Ability identification is Eleazar's power to sense whether a human or vampire has an extra gift and identify its type and strength.
Eleazar is capable of instinctively perceiving the type and strength of supernatural gifts of vampires and humans alike. He does not need to touch the other person, only be in close proximity. He considers it a "haphazard practice," as no one's gift works in the same exact way because "everyone's mind is different."
Though Eleazar's gift works on vampires and humans, he needs to concentrate harder when detecting for a human's gift, because the latent ability is nebulous. And, like Edward, Eleazar has to be in close proximity with his target to get a feel of their gifts.
Like the majority of vampire gifts, Eleazar's gift is mental; so his gift can be blocked by Bella's ability to block mental abilities. However, differently from the other mentally gifted vampires, he seems to be able to actually feel the effects of Bella's gift, instead of being blocked out.
Eleazar was invited to join the Volturi for this reason--Aro considered very useful the fact he could, potentially, determine which vampires had the strongest offensive gifts, and, therefore, determine the Volturi's most dangerous foes. Aro would often send him searching for rare talents like Bella's or Benjamin's to bring back to him therefore strengthening the Volturi. When Eleazar left after falling in love with Carmen, Aro was very disappointed as he was losing possibly the best defensive weapon the Volturi had. He only allowed Eleazar to leave in order to preserve his gift for later use, because he believed that Eleazar would return to the Volturi if he was needed.
Eleazar is the one who helped to discover Bella's own gift once she became a vampire, which was a mental shield. Unlike previous cases, Eleazar's gift was blocked by her shield; but this was enough to convince him that she was indeed using some kind of powerful mental defense. This probably also means that he can sense when his gift is being blocked. Eleazar informed the Cullens of many of the Volturi's powers before Renesmee's trial, making his knowledge invaluable to the Cullens' success.
In the movie, Eleazar doesn't seem to show any power, but his possession of this gift is implied when he tells Bella that she "[has] a very powerful gift."