Churning physically agitates the cream until it ruptures the fragile membranes surrounding the milk fat. Once broken, the fat droplets can join with each other and form clumps of fat, or butter grains. (Wikipedia)

As you turn the handle or however you do your churning, the cream goes through stages on its way to becoming butter. (Making butter)

Another side benefit of churning your own cultured butter is that you will end up with fresh real buttermilk. (Handmade Organic Cultured Butter)