In 2015 web access from mobile browsers (smart phones and tablets) was approaching 50% of web page accesses.
See more browser data.
In 2015 Google posted on the official Webmaster Central Blog,
that they would be extending the use of mobile-friendliness as a ranking signal.
It would affect rankings on mobile devices only.
Page speed and load times will also affect rankings starting in 2018. (It was not clear to me if this applied to access from mobile devices only.)
Wide pages with things like tables and long performed text (<PRE>) strings will display on mobile devices but will be reduced to fit on the screen, so hard to read. You can enlarge the view and then scroll left or right to see it, but google does not consider this mobile friendly.
They will downgrade your ranking when you search for a page that is not mobile friendly.
A page enclosed in a table with width="100%" was mobile-friendly.
width="500" was not.
A 500 x 100 pixel image is mobile-friendly
500 x 1000 Pixel Image is still mobile-friendly
The Google mobile friendly test is inconsistent.
A 600 px image on this page usually (not always) makes the page NOT mobile friendly, but on a page by itself a 600 px sometimes is mobile friendly.
A 600 x 20 px image is usually not mobile-friendly but sometimes is.
Same for a 768 x 20 px image
A non friendly table which was designed for 1,000 pixel width. -
How to make wider tables mobile friendly:
I googled around and there is no magic to make a page with a larger table "mobile-friendly" (according to google) and still have it look like a table. The solution is to convert the table to a list.
On a desktop or laptop you can hit the button below to see what it looks like on the current size window, then resize the window and hit the button again.
Test it here.