Often used to express admiration for someone else's success or achievements. Seeing his new sports car, I thought, 'Wow, he's really done well for himself!'
Pro Tip 2/3
Subjective Measures
Success is relative; what one person considers doing well might differ from another's view. She's happy teaching, even if others don't think she's done well for herself.
Pro Tip 3/3
Social Status
Can imply improvement of one's social standing, but not necessarily everyone's goal. He comes from a small town, but he's done well for himself in the big city.