If the technology under your website get too far out of date it may become a securty risk.
Try to login to your website every 2 weeks to a month and run updates. A security plugin like Wordfence will notifiy you when things need updating.
Always Back Up First
Before updating WordPress it is good to run a backup. Using a plugin like BackdraftPlus you can have backups run automatically on your website. But since they run on a schedule i.e. fortnightly they may not be the most up to date copy of your website. This is more of an issue if you frequently update your site.
Does WordPress ever update itself?
Yes bbut only within a version of WordPress e.g 4.7 in which 4.7.1 will automatically update to 4.7.2. However you need to manually update for major versions e.g. 4.7 to 4.8
If you encounter an issue as a result of an update please get in touch with your web professional.