Uptime Robot is an amazing (FREE) tool that I set up on my clients sites. It will alert you either by text, email or both that your website is down. It will also alert you when it’s back up. For a general rule I don’t freak out if any of my sites or client sites are down for 10-20 minutes or so.
Your website is stored on a server at your web host. A server is basically a super computer and every so often things happen. They might have to update the software or repair equipment. If a site is down for more then a few hours you might want to start looking into it and simply reach out to your host. Luckily they mainly do these types of software changes overnight so your end users will never know.