Life Insurance is esentially a bet that you are going to die and if you do, the insurance company pays out the money to the person who you appoint. The monthly cost of an insurance policy depends on many factors including your current health, the amount of money you want paid out, and the length of time you want to be insure for (10 years, 20 years, lifetime).
An annuity can take one of several forms. Normally, it is where you give a lump sum of money to an investment firm. The firm will then pay you a monthly payment from a certain date until you die (there are some variations of that though). The amount of the monthly payment depend on how the money is invested, when the monthly payments begin, what happens to the lump sum when you die, etc..
Insurance is basically meant to protect someone in the event you die (such as a significant other or kids). There are several reasons you might want an annuity, but the most common is to have income when you retire. In short, life insurance benefits someone else, annuities typically benefit you (but like I said, not always)