People "work on" things that they want to change about themselves, like skills that they'd like to improve or bad habits that they'd like to get rid of. "Working on" these things means improving them.
Here are some common things that people "work on":
work on your marriage
work on your attitude
work on your technique (for a skill like sports or music)
work on your self-esteem
You can use "work on ___" in either spoken or written English.