Google published a new support article today, dissecting what it means by impressions, search position, and clicks within Search Analytics reports. You can read it here:

News articles about the new help topic:
New Google help document defines Search Analytics impressions, position and clicks
How Google Reports Impressions, Positions & Clicks in Search Analytics

Some highlights:

What is an impression?

A link URL records an impression when it appears in a search result for a user. Whether or not the link must actually be scrolled into view or otherwise visible depends on the type of search element that contains the link, as described later.
In an example, they say that a URL in SERPs "records an impression when the user opens the page containing this result." The green link below a URL in SERPs, though, does not count as an impression.

Pretty basic, right? The most interesting part of the article - and the one that the news pieces I've read so far make special mention of - is the break-down of how impressions are counted within a Knowledge Graph card. Since those cards have multiple links, Google says that

...impressions are counted by URL or by site, depending on your view in the Search Analytics report.
For an example Knowledge Graph card with five links, grouping by site in Search Analytics will show one impression for the whole card. Grouping by page will show five pages with one impression each. I think that, in the past, that difference has confused a lot of people and made them wonder if Search Analytics is accurate or not.

There's A LOT more and it's VERY technical and specific to Search Analytics reports.

They go through how to read search result position, position values and their meaning, what's a click, and more. They break down almost every feature that can appear in the SERPs and what clicks, impressions, positions, and URLs mean for each of them.

They even go a little bit into image searches, which I know a lot of newbies have been asking about lately.

It's more than my tiny bird brain can summarize, so give it a read! And share your thoughts if you have 'em.