2d Colision question

I read a lot of times that many (if not all) 2d collision detection routines store, before moving the sprite, his old position. I read this is to know the collision direction. I''m writing my own routine and I don''t store the last postion. If It collides with a platform or wall, it stops just touching it. My sprites do move more than one pixel per frame. Should I store the old position? What other functions does it have? Why do I need to know the collision direction in a platforms-game (like Mario)? Thanks