Simply stated, the three characters are the Earl of Kent, the Earl of Gloucester, and Gloucester's son, Edmund. On closer observance, Kent is a loyal follower of Lear and a defended of Cordelia. He will be banished by Lear in Act I scene i. Lear will condemn him with the words, "If on the tenth day following/ Thy banished trunk be found in our dominions,/ The moment is thy death. Away! By Jupiter,/ This shall not be revoked." Kent will leave, but he soon returns in Act I, scene iv as Caius. He will not again appear as Kent until Act IV, scene vii. He will follow Lear through the King's travails for the remainder of the play.
The second gentleman is the Earl of Gloucester. He too remains loyal to the king. For his troubles he will have his eyes ripped out, tossed, blind, out of his own castle and made to "smell his way to Dover" (Regan says this to him). His story is the parallel to Lear's. He errs in choosing to believe his evil son while banishing his good son, Edgar. Edgar, like Cordelia, is banished, although he remains in the kingdom roaming the countryside as a Tom O'Bedlam.
The third character in this brief yet exceptional scene is the evil son referred to above, Edmund, the Bastard son of Gloucester. He stands quietly by while Gloucester shares the details of Edmund's birth with Kent. "...this knave came something saucily to the world before he was sent for...there was good sport at his making." He will be the cause of his father's grief. While not obvious at this moment, Edmund will show himself to be one of Shakespeare's most despicable characters.
This brief scene of 32 lines seems harmless enough. However, upon careful study, the reader will be advised to note that each of these men plays a crucial role in the plot and development of the themes of this great tragedy.
The answer to this is that the play starts with three men coming on to the stage. These three men are Kent, Gloucester, and Edmund.
Kent is the Earl of Kent. He is a nobleman who is very devoted to King Lear. He will end up sticking with Lear through all his troubles until Kent dies.
Gloucester is the Earl of Gloucester. He is the father of Edmund, who comes in at the start of the scene as well. Edmund is his heir. During the play, Gloucester, like Lear, will put his trust in the wrong child (or children, in Lear's case) and will pay the price for his mistake.