In general computing a "backup" is considered to be a copy of computer data taken at a moment in time with the intention of being able to use it to restore original systems after a data disaster, loss or corruption.
Backups have two distinct purposes. The primary purpose is to recover data after its loss, be it by data deletion or corruption. The secondary purpose of backups is to recover data from an earlier time.
The process of making backups varies wildly through different computer systems and disciplines. Most computing contracts include requirements to take and safely store data backups.
Since a backup system contains at least one copy of all data worth saving, the data storage requirements can be significant, this is especially true in cloud computing systems where storage space is at a premium, and "offline" backups may be the preference in these scenarios, in which the data is taken off the internet and stored securely elsewhere.
More on backups in general can be read on the wikipedia article here.