A person is modest if he or she is very successful but does not call attention to this.
Modest generally means "big enough but not huge" — like a modest house or a modest income. An ambitious person will not be satisfied with modest progress. Around the turn of the 17th century, modest referred to proper or decent dress and behavior especially in women. Although this is considered dated today, modest is still used for people who are shy about showing their body. If you are modest, you might wear your t-shirt when you swim.