Mobilegedon was defined in April 2015 because Google+ decided it was going to give priority in Google Search for mobile friendly (as defined by Google) websites. There were tests that developers and website owners could use to see how friendly their website is for mobile.
If you are thinking of a getting a new website, look for one that is , at least, mobile responsive. HTML websites are not the website of the future. More people are looking at websites on their smartphone to find places to eat, compare prices or find a business on a map so you have to make sure your website is mobile friendly if you want to have people look for your business on the internet.