A file is considered open when there are no pawns on it. In the following position:

the c file is open.

Open files are strategically important because they can be used to penetrate into the opponent position. Major pieces (most commonly rooks) are natural candidates to own an open file. For example, in the following position:

White owns the c file as both their rooks are on occupy a square on the c file. While ownership is important, what makes open files really valuables strategically is what we call an entry point. That is a square in the opponent side of the board where we can place one of our rooks. The best ranks entry points are on the seventh (or second) rank. Often the sixth (or third) rank offer valuable entry points in the opponent position.