The term "creature performer" and "man in a suit" are not technically job titles in the industry. It's what actors who play creatures have affectionately become known as, mainly by fans of horror, fantasy and sci-fi movies.
Everybody is different in regards to the look and skill set they bring to a performance, but at the core it's about being able to act, having an incredible amount of patience, and being physically and mentally fit. There are a lot of hours being very uncomfortable and incredibly hot in these claustrophobic creations.
Generally, there are 4 main types of performer and each have their own different challenges as an actor.
Man in a Suit - Without the luxury of people being able to see you emote via facial expressions, suit performers rely solely on physical performance. It's arguably the most physically and mentally demanding. The great Haruo Nakajima, who played Godzilla from the 1950's through the early 1970's, is the best example of a 'man in a suit'. More recently, people like Brian Steele (Hellboy II, Predators) and Douglas Tait (Star Trek, Zathura), are known in the industry for doing great work in big, heavy monster suits.
Prosthetic Makeup - Involves having silicone or form latex glued to the face and/or body of the performer. Actors who work in prosthetic makeups, like the legendary Lon Chaney and current creature king Doug Jones (Hellboy, Pan's Labyrinth), are probably the best examples of people who can completely transform into a character in prosthetic makeup.
Performance Capture - A rapidly growing way of performing characters, wearing nothing but a thin lycra suit, having little to no set and a helmet cam attached to record facial expressions. Two of the most notable in this field are Andy Serkis (Lord of the Rings, King Kong) and Terry Notary (Rise of the Planet of the Apes, The Hobbit).
Skin Work - These suits are worn by performers who play characters on children's television, for example, 'Teletubbies' or 'Yo Gabba Gabba'. The suits are normally less elaborate than ones used in film, but it's no less demanding on the actor inside.
To learn much more about the history and the performers, I highly recommend the following videos.