Hugh Fennyman is "the money"— the man who finances the plays that Mr. Henslowe puts on at the Rose. When he lights a fire under Henslowe's feet (literally) to make him pay back his debts, Henslowe lights a fire under Shakespeare's rear (his Shakesrear if you will) to write a new play.
Without Fennyman igniting the action like this, we wouldn't have a movie… and we wouldn't have Romeo and Juliet. For such a minor character, he has major influence.
Out of all the film's minor characters— and like a Shakespeare play, there are many— Fennyman gets the most dramatic scene when he is given a dramatic scene in Romeo and Juliet. He takes his role as the Apothecary very seriously. His stage fright humanizes him, after he's been a ruthless loan shark for most of the film.