Cousin Itt was a short man covered in long blond hair from head to toe, with gloved hands, owlish sunglasses, and a derby hat. He spoke in a strange gibberish (created for the TV series by recording nonsense words into a tape recorder and then playing it backwards speeded up), but all of the Addams family members could understand him, and ordinary people would begin to understand him after long exposure.
Precisely what Cousin Itt might be was never explained, keeping him a tantalizing mystery. In one TV episode, he shrinks to the size of a doll after spending too much time under a hair dryer, with Uncle Fester crying out that Cousin Itt could have disappeared altogether if he'd spent much more time under the dryer. Earlier in that same episode, Gomez asks Cousin Itt just what he is under all that hair; his answer: "Roots" (i.e. hair roots). In the animated continuity, Cousin Itt is briefly identified as being a troll, during a sequence when Cousin Itt becomes excited at the sight of a Troll Bridge before Wednesday gently points out that it is only a Toll Bridge, not a Troll Bridge, to Cousin Itt's obvious disappointment. In the film continuity, it's clear that whatever Cousin Itt might be is able to sire children with human women, as he eventually sires a son, What, with his human wife.
In the TV series continuity, Gomez and Morticia originally both claimed Cousin Itt as a relative; however, in a flashback to Gomez's and Morticia's marriage, it was revealed that Cousin Itt had dated Morticia's sister Ophelia for a while (not long after a joke centering on the idea that the Addams family and the Frump family do not believe in dating close relatives). This means that either Cousin Itt is Gomez's cousin but not Morticia's or that Gomez and Morticia are distantly related to each other as well as to Itt.
Cousin Itt's last name was never given in the series, unlike Fester Frump or Grandmama Addams or Thing T. Thing, all of whom were given a last name at least one episode (and all of whose last names are different in the film continuity).
In the film continuity, Cousin Itt is clearly identified as an Addams.