You should use a database to store data that you want to keep after the program terminates, not so much transient things like in-memory data structures. It's also best used for relational data- stuff that is logically linked together.
For developing a game, maybe storing item tables with items and stats or the player's inventory might be good candidates. Sqlite in particular is good for this because it's easily embedded and a lot of games use it from what I know.
This is oversimplifying a good bit, but it's hard to completely describe the scope of relational DBs.