Is it normal to dream of things before they happen?

I have these dreams and sometimes I remember them, sometimes I don't. But every once and awhile I'll dream of something (usually an image) and it will happen the day after or a couple days after. I uses to think it was just my mind playing tricks until once, I dreamed about a room at my grandfather's funeral that I had never been in.
It scares me whenever it happens because usually I only remember shortly after the dream and when the reoccurrence happens. Even though I have a bad memory, does anyone know why I remember these??