You're understanding of backup is pretty much on the nail. It means a multitude of things to different people. To some of us it's a copy of all documents made to a separate partition, so that we can reformat the C drive without fear of losing anything important. Others mirror the entire drive contents. Some backup to a partition, some to media like CD-R, others to remote hard drives or tape streamers.
Your concerns about storing copies outside the house are valid, particularly if you work from home and store business critical info like a client list and keeping copy info in whatever format you choose in a suitable fireproof datasafe click here may be worth your while, only you know what the information is worth and how damaging its loss would be.
As to automated backup click here for a posting on backup software, most of it can be set-up to automatically backup whatever you choose to a media of your selection at a set interval.