“I need to work on my posture.”
Your back hurts. You usually sit a little hunched over, with your shoulders forward and your back bent. You don't think that's healthy, so you think this to yourself.
I need to work on my posture.
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.
Your "posture" is the way that you stand, walk, and sit.
When a person sits, stands, and walks with a straight back, people say that this person "has good posture". When someone's back is usually "hunched over" (bent or curved), we say that they "have bad posture".