When a horse can easily carry his weight on a loose shoulder, the front leg will stay a short fraction longer on the ground so that the hind legs have more time to come under the body. As a result, there will be more jump in the gallop and with a more spacious use of the shoulder.
The connection between the fore legs and hind legs is the back. When the back muscles are loose, they can be easily stretched, what is needed to bring the hind legs under the body.
The hind legs are of course also very important, but not more than the front legs.
When all muscles groups are loose, there is flowing movement without tact-errors. From the moment that 1 muscle group is not able to prolong without tension, there comes a hitch in the movement.