Back when I just had a personal site with some code on it, I wasn't too picky about hosting. I went with cheap and simple - maybe $10 a month at the most - and usually you get what you pay for. So the site would go down for a few days a year. No big deal for me, since that's the trade offs of having low cost hosting.
Now that I have a business site, part of my job is to make sure that site is up all the time. A commerce site that is down means lost sales and upset customers. We have a really excellent full service hosting provider, but they dont monitor our website's uptime (only the network itself, and the computer is their responsibility).
The good news is that we have customers who will alert us if the site is really sluggish or down or if the MySQL database is hiccupping, but it would be better if we knew before customers started noticing en-masse. Thats when we read a geeky list of software services that looked interesting and noticed that they were using a thing called "web site monitoring" and we were all like "hmm! that sounds interesting."
Website monitors are tools that give you uptime and website-loading response times with optional notifications. Most just do uptime - so they tell you when the site is down via email, twitter, sms, etc. There are also some that load the website you run from various computers around the world to let you know if its sluggish.
At this time we're trying out Pingdom which does both response times and uptime monitoring.