Concentration is fundamental to the child's later learning. As he pours the beans from one pitcher to another, the rhythm of his actions almost lulls him into a trance of sorts. This trance pulls him into his work and he develops an intrinsic focus stronger than anything he has ever felt before. This focus translates into the concentration skills he will require as he enters the academic world. The more he scrubs tables, the calmer his body becomes, making him better able to sit through those longer lessons. A calm body and a calm mind is more willing to open and to receive new knowledge.
Coordination is built as the child manipulates those small tools. It takes a great deal of skill to manipulate those small spoons and tongs. Often, children are expected to make do with adult-sized materials in an adult's environment. The Montessori practical life curriculum scales back those utensils and skills, to make them child-friendly. Using utensils that fit the child's hand allows him to be successful and to achieve mastery. As he masters using materials that fit his own hand, he can work his way up to using the "normal" materials in his regular environment.
Along with the coordination is control. Control refers to the child's ability to control the materials and utensils he manipulates. It refers to his ability to control his body, as well. He must control his body as he moves through the classroom environment, to be respectful to his peers. Control over his body also teaches him to respect himself.
These are three of the biggest reasons why we focus so much on practical life with those three year-olds. Let them develop this foundation and then all of that academic learning will burst forth. Children who come to us later are also encouraged to spend much time in practical life in the beginning. They can still build that solid foundation and become successful in their endeavors.