If you point the board straight down the hill and keep it completely flat with the ground, you are not on an edge. From this position, if you point the board to the right of "straight down" and then lean to the right, you will be on an edge... meaning the right edge of the board will be in contact with the snow on the ground, and the left edge of the board will not be in contact with the snow in the ground.

So you will be traveling down hill on a diagonal. You can then lean left, and swing your back leg out so that the board will now be pointing to the left of "straight down."

If you point your board straight down the hill and keep it flat, you are more likely to "catch an edge" and wipe out. It will look and feel like you were tripped.

I did a youtube search on "snowboarding beginner" ...this person does a good job of staying on edge. In the beginning she has the board perpendicular to the slop grade and is leaning back. Let's call this "putting on the brakes." Also she has her left leg back, this is called riding "goofy." Most people snowboard with their right leg back, which is called "regular."

http://www.youtube.com/watch?v=t5qgGDbYa9Q

Hope that helps...