Completed air yards refers to the total distance that a thrown ball travels from:
Point A - the Line of Scrimmage
to
Point B - where the ball is caught
So, let's say that Josh Allen throws the ball to Stefon Diggs, who is immediately tackled. The pass was a 7-yard completion, meaning that the ball travelled 7 yards from the line of scrimmage to Stefon Diggs, who was immediately tackled.
So, in this case, the completed air yards would be 7 yards.
Now, what if Diggs broke the tackle and took it to the endzone?
The completed air yards would still be 7 yards, as the CAY (completed air yards) include the distance from the line to scrimmage to the point where Stefon Diggs MADE the catch. Any yards-after-completion don't get added to the Completed Air Yards equation.
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Completed Air Yards indicate how far a quarterback is throwing the ball down the field, though the stat is not at all indicative of how good an offense is.
For instance, a team that makes liberal use of pass-catching running backs (such as the Chargers with Austin Ekeler) will have a lower Completed Air Yards number than, say, the Miami Dolphins, who like to throw down the field to Tyreek Hill and Jaylen Waddle.