See this picture with three stances, the stances on the outside are with the hips closed. The middle is with the hips open. When your hips are too closed, the angle of your skate blade when you push off is too shallow, and your edge probably slips a little, and thus you don't maximise the power that you could have in your push. You're more running on the ice than skating.
When you open up your hips correctly, you grip the ice better, and don't waste any energy in slippage, so you maximise your power and efficiency of your stride.
Obviously, there's more to the stride than that, but this is what I think they mean when they say for you to open up your hips.