Theseus is kind of like the high school principal of the ancient world: he's the one responsible for making sure everybody follows the rules, for breaking up fights, even for organizing the construction of that new sports field where rival teams can duke it out. In the world of "The Knight's Tale," Theseus represents rules and order. He's full of "wysdom and chivalrie" (7), and he's also quite a conqueror, who's won "ful many a riche contree" (6).
The very first time we see Theseus it's obvious that his good reputation has spread far and wide. He's confronted by a large group of damsels in distress who've waited for two weeks at the Temple of Clemence to beg him to take revenge on Creon, a tyrant king who is refusing to let them bury their husbands' bodies (which totally breaks the Greek rules surrounding proper burial of the dead). They've obviously heard of Theseus and his reputation, and see him as the best man to take revenge on Creon. There's no way that Theseus can refuse the damsels in distress. Theseus, being the chivalrous and rule-enforcing guy he is, must make sure Creon doesn't go unpunished. Similarly, he's got to resolve the dispute between Palamon and Arcite, not only because it involves his sister-in-law, but also because it's causing civil unrest in his territory, threatening his control.
Theseus doesn't just rule, though. He also takes a lot of time to reflect on life's rules and to share his insights. The first time he does this is when he finds Palamon and Arcite duking it out in the forest and hears the cause of their fight. He connects this dispute to the general rule that Love is a greater god than any other, and reflects on all the stupid things that people are willing to do for love.
Similarly, when Arcite dies, Theseus can't let it pass un-commented-upon. He connects Arcite's death to the general rule of life that everything dies, and holds this out as evidence of a supreme being who has an orderly plan for his creation. From Theseus's reflections arise an insight about his character: he's a guy who likes to make abstractions – to deduce general rules from specific circumstances. He's something of a philosopher-king.
All of this isn't to say that Theseus lives his life in an ivory tower with his head in the clouds. No, Theseus uses his insights to figure out how he and others around him should act. When he interrupts Palamon and Arcite's fight, he decides to have mercy on them because the rule of "discrecioun," or making decisions using good judgment, is to distinguish between things. Palamon and Arcite are acting with humility, Theseus reflects, so he should not treat them the same as someone who's acting with pride. Similarly, from the rule that everything dies, Theseus deduces that the proper response to death is to keep on living. For this reason, he orders Emily and Palamon to marry.
So in Theseus, we have just about as ideal a ruler as we can get. He not only has the power to rule, but the wisdom and fairness to rule justly. We also have a character who comments upon the events that are happening in the story, reflecting on their possible meaning. In this, he resembles us, the reader, providing a built-in interpreter for "The Knight's Tale." (For another Chaucerian character who plays the same role, see the Host.) We may not always agree with his interpretations, but he certainly forces us think, and think hard, about the meaning of the events that happen in the tale.