Basically, what's a disk "failure"? A file gone missing? The whole filesystem gone missing?
How are they caused, and what is usually done by the system (or the user) to fix the failure?
A "failure" is when the hard drive becomes completely inoperable. Data loss may occur before such a failure, but generally, a failure is when the drive stops working completely. This applies whether the disk heads crash onto the platters, the onboard electronics fail, or anything else renders the disk unreadable. If data loss occurs, but the remaining contents of the drive can still be accessed, a failure has not occurred.
Typically, when such a failure occurs, the drive is replaced and any data is restored from backups.