Branch = man / Vine = Jesus / Fruit = character traits of the Spirit - those who hear and accept Jesus
The Christian is called to not simply claim to be connected to Christ, but to actually be connected daily for refreshment, encouragement, nourishment, obedience. You don't have to be a horticulturalist to know that a branch not connected to it's vine will grow no fruit...it'll grow nothing and eventually die. Not surprising.
Grapes grow in bunches, where one sprouts so sprout many. Not only this but many branches grow as well, producing enough grapes to profit the gardener. A picture of healthy, productive, sourced, fruit-bearing, multiplying, profitable community.
No, a branch can't bear fruit alone, it needs the Vine - and it seems that the Vine is seeking to grow many healthy branches to produce lots of fruit - to honor the Gardner.
'...I have told you this so that my joy may be in you and that your joy may be complete.'