In Croc's initial string of appearances — a Detective Comics story arc that culminated in Jason Todd adopting the mantle of Robin — he was depicted as an unnamed, shadowy figure in a trenchcoat. A ruthless criminal who wants to become the crime kingpin of Gotham City, Croc works behind the scenes using methods like sniping to eliminate his criminal competitors. He briefly unites a small army of Batman villains under his leadership. When Batman finally confronts his mysterious foe, the villain is revealed to have a massive physique and reptilian appearance. It is then revealed that his real name is Waylon Jones, born with a form of atavism that imparted him with reptilian traits. His parents grew to loathe their child's hideous appearance and brutal behavior. While still an adolescent, his father abandoned him in the wilderness. Croc survived, becoming a career criminal. Batman and the new Robin defeat him after a desperate battle.

In these original, pre-crisis appearances, he resembled a powerfully-built man covered entirely in green scales, but was still basically human in his facial proportions and build. Over the years, writers have discarded the original conception of Croc as a crime lord; for instance, Killer Croc was originally depicted as gunning down Jason Todd's parents (this was later retconned to make Two-Face their murderer). His appearance and personality have become increasingly bestial, explained in the comics that his disease has slowly robbed him of all identifiable human traits. In his most recent appearances, he has an elongated snout and tail.

Killer Croc was originally an inmate at Arkham Asylum, who was born with a rare skin disorder that deformed him to look like a crocodile. He became an experiment subject for Jonathan Crane's (later to become known as the Scarecrow) Fear Aversion therapy program. Croc grew up in Arkham Asylum and was released when Ras' al Ghul's ninjas released him along with his inmates and the Scarecrow himself. Croc was one of the inmates to escape the incident in the narrows and joined a group of inmates that fled underground with the Scarecrow. There Scarecrow continued to experiment on Croc by injecting his Fear Toxin into parts of his body.

(Source: Wikipedia and Batman Wiki)