It is important to regually inspect your website as this could cause issues down the track.
Go throught all your website pages to see if you find any errors, missing content such as text/images or if the page is showing up when someone tries to view it.
Just like your antivirus software on your PC you can do secuirty scan on your website. If your website uses WordPress there are many great secuirty plugins which can do the job. The security plugins will scan your website for vulnerabilities and then provide you with the recommended actions to take. If you speak to yout hosting provider they may allow for scan from their end too.
Run website backups
If your always updating your website with fresh content you should then regually run backups of your website. This can be done with a plugin or if you have access to Cpanel their is a automated backupsoftware which will do this for you. For more infomation speak to your hosting provider.
Update plugins and themes
If your website runs WordPress you should then update your plugins and themes when they become available. As this patches any holes in them which hackers can use to get into the backend of your website. (But before you do any updates make sure you backup your website as sometimes plugin update could cause some issues with your website)