A failure describes an issue with the computer or a device that prevents it from functioning correctly. For example, when a hard drive fails (hardware failure), it prevents the computer from booting and working again until it's replaced.
Although a failure is associated with hardware, any problems with software may also be called a software failure. With most software failures, you'll usually encounter an error to indicate the type of problem. A general failure is a non-specific failure that could be caused by software or hardware.