A backup service is a tool that automatically (at an interval that you specify) creates backup copies of specified or even every single file on your computer. The idea is that if your computer crashes, you would be able to restore the backup and pick up right where you left off.
Data backup services take your memory out of the equation. Once you set them up one time, backups will be automated, without you having to remember to push something to the cloud. They are generally pretty inexpensive for personal use.
Like the cloud services, these are just a fraction of what is available. Here's another Wikipedia chart with more detailed comparisons.