What do people usually ask letter writers to emphasize in a letter of reference? I hear that a lot of letter writers to let them know things things you would like for them to "highlight in your application". 

What do most people ask their letter writer to emphasize? Is it personal anecdotes between themselves and the letter writer? their own work ethic? their personal theoretical contributions to projects?
People are sometimes asked for such things, if for no other reason than to remind the writer about what the applicant has done. But, there is a more important consideration. 

The fundamental requirement of a supportive letter is for the writer to make a prediction, even if not explicitly stated, that the subject of the letter is both highly qualified (the past) and has great prospects for success (the future). 

When possible, provide some evidence, especially about things that might not show up in a CV. 

Everything in the letter needs to support that primary goal, no matter how stated. Anecdotes might help, past research, great questions in class or the office (curiosity). But make sure that the main goal is addressed. Otherwise the letter is just noise. 

Qualified (check). High likelihood of success (check).