In Homer's Odyssey, who is Theoclymenus and why should Telemachus treat him kindly?

Theoclymenus is a seer who is fleeing Argos for killing a man of his own race. He tells Telemachus that the kinsmen of the murdered man seek to avenge themselves on him; this is why he lives in exile.
Theoclymenus is actually a very important guest; as he is a seer, he can see the future and interpret omens. If Telemachus treats him kindly, he will benefit from Theoclymenus' psychic abilities. In the story, Theoclymenus' clairvoyant skill is demonstrated when he observes a hawk fly by Telemachus' right hand. The hawk is clutching a dove in its talons, and in mid-flight, it tears the feathers of the dove off. The feathers fall between Telemachus and the ship. Theoclymenus interprets this as a good omen. He tells Telemachus that he, Telemachus, will remain a powerful man and that no house in Ithaca will be as royal as his own.
As time progresses, Theoclymenus becomes more and more important to Telemachus. His ability to interpret omens is a gift that encourages Telemachus and those who are faithful to Odysseus' house. In Book 17, Theoclymenus tells Penelope (the wife of Odysseus) that he can divine the future. He tells her that her husband "himself is even now in Ithaca, and, either going about the country or staying in one place, (and) is inquiring into all these evil deeds and preparing a day of reckoning for the suitors."
In Book 20, Theoclymenus prophesies that the suitors will eventually meet their doom:

But Theoclymenus said, "Eurymachus, you need not send any one with me. I have eyes, ears, and a pair of feet of my own, to say nothing of an understanding mind. I will take these out of the house with me, for I see mischief overhanging you, from which not one of you men who are insulting people and plotting ill deeds in the house of Ulysses will be able to escape.

From the text, we can see that Telemachus' welcome of Theoclymenus is not misplaced. His kind treatment of his exiled guest has earned him the loyalty of a seer who has psychic abilities. At each stage of the mission to reclaim Odysseus' household, Theoclymenus uses his clairvoyant abilities to encourage Telemachus and his allies. So, Theoclymenus is an asset to Telemachus.