They are retirement investments which defer compensation over time. There are several different types, but they are designed to allow you to reduce some risk of death too soon or too late after retirement. Some allow you to pass on benefits to surviving family.
Annuities are a type of insurance. You pay fees at the time of deposit, and, in exchange, there is a guaranteed account balance, no matter what happens with underlying investments.
Annuities are insurance policies that are set up to start paying you a designated amount after so many years, which you determine when you take out the annuity.