The big willow tree swallowed Pippin and Merry and threatened to suffocate them. Frodo and Sam were frantically yelling for help when they heard someone carelessly and happily singing a ludicrous little song and making all sorts of noise as he stomped. The person listened to the hobbits' plea and, taking their plea seriously but not urgently, commanded the willow to release them, which it did.
Whatever he was, one thing was certain: He was powerful, as evidenced by his power over the mighty willow tree. He was so powerful that, at the Council of Elrond, it was suggested that he be given the One Ring, for he was invincible within his realm and, unlike every other creature of Middle Earth, the Ring had no power over him.
Bombadil exercised his power ruthlessly: Spending his days rambling about his lands, making merry, singing silly songs and laughing with the plants, and listening to his lady Goldberry sing. When called upon, he was a gracious host: Tending the hobbits' ponies, providing the hobbits with soft slippers and splendid meals, sitting beside them like a father as the hobbits fell asleep, making sure that they rested well on soft down pillows and snow white blankets, and lastly getting them safely past the wretched barrow-wights as they continued their journey.
At one point during his visit, Frodo asks Goldberry about Bombadil's realm, “Then all this strange land belongs to him?” Significantly, Goldberry replies, “No indeed! That would be a burden. The trees and the grasses and all things growing or living in the land belong each to themselves.” But then she goes on to say that Bombadil is the master. In his realm, Bombadil has nothing, but, in an illustration of the paradox of true poverty, he has power over everything.
It's a paradox illustrated in the lives of the saints, especially St. Francis who, through his intense love of poverty, obtained power over everything, from fire and water to Islamic sultans. Those who care nothing for power, obtain ultimate power.