Ever watch a ballet? Maybe on TV or the stage? Watched shows like "So You Think You Can Dance"?
Those dancers can create this amazing illusion of weightlessness. They way the glide across the floor and suddenly they're spinning on a single leg or leaping over the heads of other dancers. Maybe they're spinning AND leaping.
They're able to create this effect because they have mastered their relationship with the floor. If you watch each step they take, no matter how fast or slow, the articulation through the foot shows connection, a push through the floor, that allows them to rise above it so easily.
Take a look at this video for an example, and really watch their foot contact with the ground:
Most people who don't think much about what their feet are doing as they are standing or walking around. If you ask someone to squat without any instruction, you often see them sit their hips down any which way and many will end up in what I call the "gargoyle squat."
So initially, we tell people to put their weight back in their heels. We ask them to spread the floor and spin plates with their feet. Many will take these cues to an extreme and lift their toes off the ground or roll their feet so the big toes pops up. These exaggerations are tolerated at the beginning so that athletes can become aware of differences in balance when emphasis is put on different parts of the feet.
But as a person advances, you want to see them start to bring those exagerations back in and actualy use full foot against the floor to create movement. The balance within the footprint may change, but pressure is still distributed. Watch the lifter in the following HOOKGRIP video and see how her center of gravity changes through the lift, but as long as she is moving the bar up, the foot is pushing into the ground:
You can also often tell a person's body awareness by how they box jump. Even if you can't SEE them rolling their weight from their toes to support in the full foot. Many people still trying to figure this dynamic out land totally flat footed and you hear the smack with every landing.
Thinking more about your foot contact with the ground, and working with gravity, can help you increase the quality of your movements. They can smooth out your steps in heavy carries, make your squats more stable, and increase the force you produce with jumps and the Olympic lifts.