Your ability to control your core is important to stay down and through your golf swing. You may hear how it is important to maintain your angles throughout your swing. If you lift or come out of your angles, you'll miss hit shots.
If your core, including the pelvis and hips are weak and unstable, then you'll start to use other parts of your body to hit the ball. Most of the time, you'll end up flipping your hands through impact if your core doesn't stabilize, resulting in thin or fat shots.