Halbarad, like Aragorn, is a Ranger of the North. This means that he is a descendant of the Men of Westernesse, and a kinsman of Aragorn's. He and the other Rangers have the lonely task of patrolling the wildernesses to keep an eye on evildoing in this otherwise sheltered realm of Middle-earth (bear in mind that the Shire is also in the north; we're sure the hobbits need a lot of protecting, since they are so unaware of the dark forces of the larger world). Halbarad and his men, the Dúnedain, are the "Grey Company" that Tolkien mentions in the title of Book 5, Chapter 2.
When Halbarad catches up with Théoden's escort near the banks of the River Isen, Aragorn is amazed to see the Dúnedain, the Rangers, because he never sent for them in the first place. It turns out that it wasn't Aragorn who sent for them, but Galadriel, who issued the call to Rivendell: "Aragorn has need of his kindred. Let the Dúnedain ride to him in Rohan!" (5.2.40). But whoever called them, it doesn't matter—Théoden welcomes them with open arms: "If these kinsmen be in any way like to yourself, my lord Aragorn, thirty such knights will be a strength that cannot be counted in heads" (5.2.23).
Halbarad basically joins the characters of The Return of the King to give Aragorn someone to talk to as he plans his future strategies. Halbarad is like Aragorn in all ways, in fact, so when Aragorn talks to him, it's as though Aragorn is talking aloud to himself. Gimli comments that the Rangers are "grim men of face, worn like weathered rocks for the most part, even as Aragorn himself" (5.2.37). But, Gimli adds, "even as Aragorn they are courteous, if they break their silence" (5.2.38). They go mostly unadorned with any special kind of jewels, except that each Ranger wears a brooch shaped like a star on his left shoulder to clasp his cloak. (For more on that star, see "The Seven Stars" in "Symbols, Imagery, Allegory.")
When Halbarad and the Grey Company arrive at the Dark Door to the Paths of the Dead, Halbarad announces: "This is an evil door [...] and my death lies beyond it. I will dare to pass it nonetheless" (5.2.134). Halbarad's willingness literally to go through death for Aragorn emphasizes the kind of loyalty that Aragorn is capable of commanding. Already, his kingliness is starting to come through as he gets closer and closer to Minas Tirith. Sadly Halbarad does die beyond that door—in the Battle of the Pelennor Fields. But Elladan and Elrohir quickly fulfill his role as sounding board for Aragorn.