Look to where you want to go, not where you don't want to go! Your body follows the head, so focus on looking toward and past where you want your bike to end up.
Where you focus your eyes is an important factor in choosing which line to take. It's tempting to look right in front of your wheel, but it's better and safer to look at least 15-20 feet ahead (depending on how fast you're going) to scan the trail. When you look down rather than ahead, it's more difficult to anticipate what's coming and react to obstacles or tricky trail sections as quickly, and you'll be less likely to roll through them smoothly.
When cornering, look as far ahead as you can see toward and then past your exit once it's in sight. The shoulders will follow the head, thus initiating the turn, and making it easier to lean the bike through the corner.
The eyes are important when climbing as well. When you look down to your front tire, the upper back tends to round and the chest collapses, which makes breathing more difficult. Sit up tall, relax your arms, look ahead to scan the trail and break the road or trail into sections, which can help mentally on long climbs.
To learn more, check out this video from GMBN: