Backups are copies of your website's files, database and email that are kept separately, so if something goes wrong you can restore everything to a working state.
Things that can go wrong more often than people expect: a plugin update breaks your site, a hacker defaces or deletes content, you accidentally delete something important yourself, or the server has a hardware failure. Without a backup, recovering from any of these can mean rebuilding your website from scratch.
Most hosting plans include some level of automatic backup, but it's worth checking exactly how often backups run and how far back they go, since this varies by provider and plan. For anything business-critical, it's good practice to also keep your own periodic backup copy downloaded somewhere safe, rather than relying on a single source.