does it really insure your life? or just that things will go ok after your life?

just your assets..lol.

because it not life assurance

You have car insurance for when anything bad happens to your car. House for your house and so on and so on. Life Insurance if for when something bad happens to your life, like it stopping.

Because people wouldn't buy something called "Death insurance"

because your family is insured to have a nice life without you.

They call it life insurance because you take out coverage on your life. You are insured while you are alive.

When you die, your beneficiary is paid out the life insurance proceeds after a claim is made on your life.

Proceeds are usually paid free of any federal income tax.

Term life insurance is usually the least expensive type of life insurance, because it does not build any cash value within the policy, you pay only for the life insurance protection.

For more information, Learn how term life insurance works.

I hope that helps!