It is all about learning edge control - how much pressure to apply and when. Beginners tend to put too much pressure on the edge and worse, lean back when they are scared. They also tend to look down too much - look where you want to go (it won't seem as fast that way either).

Gradually elongating your turns as you go down the slope builds your confidence/comfort level in going straighter at faster speeds - your mind/muscles learn to apply consistent gentle edge pressure. When it really flattens out, you'll ride mostly toe or heel with very, very slight edge, changing more because of tiredness than anything else.