An "insurance company" sells insurance, which is a kind of protection against bad events. For example, a health insurance company will pay for your medical bills if you get sick or injured. Common types of insurance include:

• health insurance
• car insurance
• homeowner's insurance
• life insurance (money that gets paid to someone's family if they die)

People talk about "insurance companies" like this:

The damn insurance company said that my policy didn't cover flood damage, so I didn't get anything.