Bereavement Airfare is when an immediate family member, or a loved one, has died in another city and you need to purchase airfare on short notice, - that is a Bereavement Fare. In many cases the airline companies will provide airfare up to 50% off.
You have to call the airline companies directly, as you cannot purchase it online. Usually, you must provide a copy of the death certificate, and they will give you a few days to provide it.
I recommend you first check out a last minute deals site, such as www.Kayak.com to see that the price is for the cheapest flight you can get. You can then compare prices.