Mr. Jorkins is the business partner of David's employer, Mr. Spenlow. He exists mostly as a boogeyman for Mr. Spenlow to refer to whenever an employee asks Mr. Spenlow a favor. When David asks to be released early from his apprenticeship (because he needs the money his aunt paid so that he can support Miss Betsey now that she has gone broke), Mr. Spenlow says that he would consider it, but Mr. Jorkins would never allow it.
When David actually meets Mr. Jorkins, he realizes that the man isn't a tyrannical bully who won't allow Mr. Spenlow to do anything kind to his employees. Instead, Mr. Jorkins is a pretty mild, easy-going guy who doesn't like getting too involved in the business. Mr. Spenlow has just been using Mr. Jorkins's name as an excuse so that Mr. Spenlow doesn't get into difficult confrontations with people when he tells them no.
This mildness of character is actually a problem once Mr. Spenlow dies suddenly. Mr. Jorkins hasn't got the kind of temperament to run a law office properly. Indeed, the business basically tapers off and dies with Mr. Spenlow because Mr. Jorkins just isn't that interested in work.