We can't be sure that River has revealed all the ways she uses her diary but those we do know include:
- Identifying the Doctor. She has pictures of all the incarnations in his first regeneration cycle, up to & including the Eleventh Doctor. She didn't have a picture of -- & therefore didn't recognise -- the Twelfth Doctor. (See "The Husbands of River Song".)
- Keeping track of her encounters with the Doctor & of her timeline in comparison with his. (See, for example, "The Impossible Astronaut".) She does this to avoid giving him "spoilers" -- advance information about his personal future.
- Recording information about alien species, such as the Weeping Angels. (See, for example, "Monster File: Weeping Angels" (webcast).)
- Notes on piloting the TARDIS. (See "The Eternity Clock" (game).)
Note: Because River is careful to avoid giving "spoilers" (to others, as well as to the Doctor) & is secretive as a result, this list is almost certain to be incomplete.
For additional detail, see River Song's diary.