1. expert; learned person
電車のことなら、弟はまるで博士だ。When it comes to trains, my little brother is a real expert.
2. doctor; PhD; Dr.
お疲れ様です、博士。Thank you for your hard work, Doctor.
3. instructor at the imperial court (ritsuryō period)
4. pitch and length marks (to accompany a Buddhist liturgical chant, etc.)