The first appearance of the symbiote was in Marvel's Secret Wars comic line, in which the alien suit bonded to Spider-man, granting him greater power. After awhile, Spider-man learned that the suit was alive and taking over his life, so he had it removed a few times, as it kept coming back to him.
Eventually the symbiote found another host: frustrated, angry newspaper reporter Eddie Brock. The symbiote bonded with him, and together they became the super-villain known as Venom, who had the same powers as Spider-man, but stronger. Because the symbiote and Spider-man were allies for so long, Spider-man spider sense never registers Venom as a threat, making him even more dangerous. The symbiote-infected human always referred to themselves in the plural first person, saying "We" instead of "I".
Once, when Brock was separated from the symbiote and sent to prison, it returned and broke him free, making them Venom again. Brock inmate, the psychotic serial killer Cletus Cassidy, involuntarily bonded with some of the symbiote's spawn, and they became one of Spider-man's most dangerous foes ever: Carnage. Carnage was even more powerful than Spider-man and Venom put together, showing that the symbiote sapped power from each host and gave it to its offspring.
The symbiote's two main weaknesses are sound vibrations, and extreme heat.