Any website can be loaded on a browser on your phone and at some point whilst browsing the internet you've probably encountered having to use a desktop website on your mobile phone. The text is tiny so you have to pinch to zoom in but then it's difficult to see the other content on the page. You try to click a link but you click the wrong one by accident because the links are close together. You load a page to be greeted by the message "this feature cannot be run on your device". It's frustrating to say the least and isn't a great browsing experience.
A mobile friendly website quite often will only require a vertical scroll, meaning you don't need to scroll across to see all the content on the page. Rather than a big menu with tiny links, you should be met with whats referred to as a burger menu ( "" the three lines you tap to open a menu). Once opened, the links in the menu will be nicely spaced out and won't lead to you tapping the wrong link. The page should load fairly quickly too and shouldn't be image and video intensive like a lot of desktop sites. Features, such as videos or on page quizzes should work and be compatible with mobile browsers. In essence, to be considered mobile friendly, a website should be fully operational on mobile and be easy to use.
Most people and companies will want maximum exposure for their websites. Years ago one aspect for increasing visibility was ensuring you were in the Yellow Pages and other popular telephone directories, as people's first port of call when requiring a service was to check the phone book.
Nowadays, one of the first places people look for a service is on their mobile. If they find you on Google, or an alternative search engine, they may choose to view your website to get an idea of who you are. If your website doesn't work on mobile, the visitor might be tempted to navigate away and potentially visit a competitors website.
If your website isn't mobile friendly, you will also most likely be penalised in rankings by search engines, leading to competitors appearing above you in search results. Going back to the phone book analogy, companies would deliberately name themselves "A1 PLastering", as an example, so that when companies were listed in alphabetical order theirs would be one of the first you saw. If your company is seen first, either in a phone book or on a search results page, you are increasing your chances of being chosen by a customer over a competitor.
Lastly, mobile devices are only going to become more dominant in the future. Most businesses don't intend on closing or losing business imminently and having a fully mobile friendly website is one way of future proofing your business. This, in addition to the other benefits such as an increased chance of appearing higher up in search results and an increased chance of converting a visitor who has landed on your website, is why a mobile friendly website is so important.