An animal that is venomous produces poison. Also, people act in a venomous way when they are cruel, evil, or deliberately harmful.
Both senses of venomous have to do with poison. The first meaning is literal: if a venomous snake bites you, you could die. Venomous animals are extremely dangerous, and their bite requires immediate medical attention. For people, being venomous is a little different. Spreading lies is venomous. Stealing someone's significant other is venomous. Anytime someone is being destructive on purpose, it's venomous. For people, venomous means something close to villainous — being venomous is like spreading metaphorical poison.