What is Depth in Games?

What is “depth” in games?  I have searched the Internet for “strategic depth” and found surprisingly little in the way of definition.  Lots of people use the term (or just “depth”), but they don’t explain what they mean.  It’s another of those “everyone knows what it means but does not define it”.

I have since found that the word “strategic” can be a cause for much angst and debate, so perhaps we should just talk about “depth”.  What gives games depth (or what makes games “shallow”)? 

Which games have depth?  I think most people would agree that chess and go are deep games.  And that Candyland and Tic-Tac-Toe (Noughts and Crosses), and most “social network” games are not at all deep.  Depth apparently has something to do with the complexity of decision making.

Perhaps it has something to do with the number or type of choices presented to a player.  If you need a jumpstart in that direction you might look at “How Many Choices are Too Many” http://gamasutra.com/blogs/LewisPulsipher/20111025/8731/How_Many_Choices_is_Too_Many.php which includes many comments as well.

So what is “depth” in games?