Views are the amount of times a video has been watched by other users. They are essential to how YouTube works.
About
Views have been around since the beginning of YouTube. The more views a video has, the more money a YouTuber is likely to get, because advertisers pay to have their ads shown during videos of those with high view counts. Some say you need to have a minimum of one million subscribers on YouTube to consider it a paying job as a high amount of views can make you gain that many or more subscribers and especially since 2017, the year advertisers are only featured on what is considered to be "Family Friendly" videos.
History
Originally, the term "viral" was used to define a video that had over 1 million views. Nowadays, the term is used more to identify videos with a view count of over 3 million rather than 1 million, because it is much more common for videos to get 1 million views these days.
301 club
The term "301 club" was widely used in the 2011-2015 era of YouTube. It referred to a glitch in the way YouTube calculates views when a video is first posted due to YouTube checking for illegitimate views. For a while the view count is stuck at the number 301, but eventually it is updated. YouTube eliminated this feature in late 2015 as they found a more convient way of checking for "fake views"
1 billion views
A video had not reached 1 billion views until 2012. As of 2017, Despacito by LuisFonsiVEVO is the most watched video on YouTube, with over 4 billion views. However, videos are hitting 1 billion and 2 billion views much faster than they used to. Good examples are KatyPerryVEVO and TaylorSwiftVEVO, which each have two videos with over 2 billion views.