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—”
>
><sub>*Harry Potter and the Deathly Hallows*</sub>
> 
> 
> 

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.”
>
><sub>*Harry Potter and the Half-Blood Prince*</sub>

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.