Risk analysis is a method to determine how much risk is involved in something. In testing, it can be used to determine when to test something or whether to test something at all. Items with higher risk values should be tested early and often. Items with lower risk value can be tested later, or not at all. It can also be used with defects. Severity tells us how bad a defect is: "how much damage can it cause?" Priority tells us how soon it is desired to fix the defect: "should we fix this and if so, by when?"
Defects with High Severity and Priority are tested first.