Demetrius is the “worthy gentleman” that Hermia’s father Egeus wants her to marry instead of Lysander, the boy she loves.
Lysander explains that Demetrius is not right for Hermia because he is in love with someone else—Helena.
Demetrius, I'll avouch it to his head,
Made love to Nedar's daughter, Helena,
And won her soul; and she, sweet lady, dotes,
Devoutly dotes, dotes in idolatry,
Upon this spotted and inconstant man. (Act 1, Scene 1)
Demetrius is an Athenian, and he seems to be very good-looking. Helena is certainly obsessed with him. There is no specific physical description of him (other than that he is Athenian), but there are plenty of descriptions of his character.
Demetrius gets involved in the mishap in the woods where Puck mixes up the lovers. Previously, Demetrius was completely in love with Helena and had no eyes for Hermia. Puck made him think that he was in love with Hermia instead. When they wake up and leave the woods, a puzzled Demetrius explains to Egeus that he is not in love with Hermia.
But, my good lord, I wot not by what power,--
But by some power it is,--my love to Hermia,
Melted as the snow, seems to me now
As the remembrance of an idle gaud
Which in my childhood I did dote upon … (Act 4, Scene 1)
He appears to be an honest and upstanding man, matching the other descriptions of his character. He does not try to marry Hermia just because her father wants him to and it would enrich him. He is in love with Helena and he is loyal to her instead.
Demetrius may seem to be "inconstant" as Lysander said, but he is really in an impossible situation. He seems to be quite a catch, and Hermia's father really wants him to marry his daughter. Helena really wants him too, though. He must be very good-looking!