The main difference between a single phase and a three phase connection is that a three phase connection will be able to handle a larger load.
To make it easier to understand, think of a highway with a single toll booth and a highway with multiple toll booths.
In the single toll booth scenario, one car can pass through the toll booth one at a time, where as in the multiple toll booths scenario, multiple cars can pass through the toll booths at a time.
Similarly, lets assume that the single phase connection is the single booth, and three phase as the multiple booths. In a single phase connection, there is a limit as to the maximum amount of energy load it can handle. A three phase connection is therefore appropriate for customers who need to be able to draw more energy from the grid at a particular point in time.