An impression is when a user sees an advertisement. An impression happens any time a user of an application with ads on it opens that app or website and an advertisement is displayed. It does not matter to the marketer or the advertising platform whether that user noticed the advertisement.
Impressions occur when the advertisement is displayed to a user. An engagement occurs when a user interacts or engages with that advertisement. One way in which a user can engage an ad is by physically clicking or tapping the ad; this would be considered a click.
In general engagements and ad clicks are considered to be more valuable than just impressions. This intuitively makes sense for reasons in which you can likely piece together yourself!
Reach is the total number of unique people who see an advertisement. Whereas impressions are the total number of times an advertisement is displayed, no matter if it was clicked or not.
Ad impressions are important in the world of advertising because it's one of the most popular methods in which advertisers pay ad platforms (Google AdWords, Facebook, LinkedIn, etc.) for displaying their ads. Generally charged on a Cost per Mille (CPM) basis, advertising formats tend to charge per thousand impressions. This means that it's essential for advertisers to know how many impressions a CPM advertisement generates to understand the total campaign cost.