In short
FMEA is an analysis method that systematically evaluates potential failure modes, their effects and causes in a product or process, and plans actions by risk priority.
In FMEA each failure mode is rated for severity, occurrence and detectability. This rating determines which risks to address first.
Design FMEA addresses risks in product design; process FMEA addresses risks in the manufacturing process. FMEA is a living document and should be updated regularly with failure and complaint data from the field.