AND expresses ADDITION: One idea is added to another.
Anne was reading a book and I was studying German.

BUT also brings equally important ideas together. The second idea CONTRASTS with the first.
I tried to go to the gym but I was too tired.

OR also brings equally important ideas together, but the ideas are ALTERNATIVES.
We can go to the beach tomorrow or we can go on Sunday.

Addition, contrast and alternatives:

And, but & or