Annualized failure rate is a measure of how likely something is to break or stop working during a year. Imagine if you had 100 of the same kind of thing and you were given a whole year to see how long they would last. You start counting the number of things that break during the year and you end up with a number at the end of the year. This number is the annualized failure rate of that product. It's a way of measuring the "reliability" of something, which tells you how long it can be expected to last.