He did not trust himself to have more power
As a young man, Dumbledore was tempted by the idea of power over others. It’s how he was drawn in by Grindelwald’s anti-Muggle beliefs (that and his romantic infatuation with Grindelwald, I suppose). As such, he felt it was too dangerous for him to be in a position of responsibility in the magical community:
“Years passed. There were rumors about him. They said he had procured a wand of immense power. I, meanwhile, was offered the post of Minister of Magic, not once, but several times. Naturally, I refused. I had learned that I was not to be trusted with power.”
“But you’d have been better, much better, than Fudge or Scrimgeour!” burst out Harry.
“Would I?” asked Dumbledore heavily. “I am not so sure. I had proven, as a very young man, that power was my weakness and my temptation. It is a curious thing, Harry, but perhaps those who are best suited to power are those who have never sought it. Those who, like you, have leadership thrust upon them, and take up the mantle because they must, and find to their own surprise that they wear it well.
“I was safer at Hogwarts. I think I was a good teacher—”
Harry Potter and the Deathly Hallows
He may also have viewed it as a high calling
He also seems to view it as one of the most important things a talented wizard can do:
“I am surprised you have remained here so long,” said Voldemort after a short pause. “I always wondered why a wizard such as yourself never wished to leave school.”
“Well,” said Dumbledore, still smiling, “to a wizard such as myself, there can be nothing more important than passing on ancient skills, helping hone young minds. If I remember correctly, you once saw the attraction of teaching too.”
Harry Potter and the Half-Blood Prince
Of course, he’s talking about a sensitive subject here, and to Lord Voldemort no less, so it is possible he is not being entirely honest. Nonetheless, few roles could be a greater responsibility than having to care, for the better part of each year, for a generation of Britain’s young witches and wizards: ensuring their education, protecting them from Dark Magic, and various other duties.