In the context of jumps and spins, there are two places where you will find yourself looking to the future, and they map onto two places where you should do the same in ordinary life.
The first is right before you step into a spin. You usually set up a spin from back crossovers and then hold a back inside edge for a moment right before you step onto your spinning foot. Before you step onto that spinning foot, you ought to be looking at the spot where you intend to center your spin. You need to have that spot in your vision before you step into it, but as soon as you've stepped toward it, your eyes need to move up "to the present" so that your body will be straight and your spin will be fast and centered.
The same can be said of the entrance to some jumps, actually. Most of the time, people enter waltz jumps or axels from backwards crossovers and then turn around and step forward into the jump. There's a moment before you turn around where you just look straight ahead, away from the direction of travel. That's the moment when you are "looking to the past". But then, just before you step forward, you look over your shoulder and check out the place where you are about to jump.
Life takes planning. Even the simple things have to be thought through before you do them, and you don't want to act rashly without looking. On freestyle practice sessions, not looking forward may get you into a head on collision with another skater. At work, not planning your day well might cause you far bigger problems. This is the realm of task lists and thinking before you speak.
But there are times when you need to look forward even more intensely. Sometimes you want to do something really big, something harder than your average task, and just planning ahead isn't enough. In those cases, you may need to hyper-focus on the goal you are trying to reach while you are on your way to it. Double jumps are like that.
In order to get the maximum rotation on double jumps, you need to turn your head in the direction of your rotation and "look to the future". It seems so unintuitive after you've spent so much time working on keeping your head straight on all your previous jumps and spins. But this time, that little bit of extra reach helps you get the hard stuff done.