Albus Dumbledore is the (former) Headmaster of Hogwarts School of Witchcraft and Wizardry. He is also renowned as the only wizard that Lord Voldemort fears.
How did he come to be such a powerful and respected member of the wizarding community?
According to Dumbledore's Chocolate Frog Card
ALBUS DUMBLEDORE: Considered by many the greatest wizard of modern times, Dumbledore is particularly famous for his defeat of the Dark wizard Grindelwald in 1945, for the discovery of the twelve uses of dragon’s blood, and his work on alchemy with his partner, Nicolas Flamel. Professor Dumbledore enjoys chamber music and ten-pin bowling.
Given the nature of the Chocolate Frog Card, it seems likely that it mentions the achievements he is best known for.
In addition, we also know that Dumbledore is supposed to be the only Wizard Voldemort was afraid/apprehensive of. He led the Order of the Phoenix, and subsequently seems to have led the anti-Voledmort war effort in both wars against the Dark Lord - an achievement that would be post the Chocolate Frog Card text given above.
The question is like 'Why is someone better at something as somebody else?'
Dumbledore was a very talented boy who was interested in many things concerning magic. We know at that he was at least interested in:
In almost all of these cases he did great work which were accepted by all of the magical community like his 12 uses of dragon blood in alchemy or his teaching in Hogwarts.
One work of his, that made him known all over the world was his victory against Grindelwald in a magic duel. Grindelwald, having been one of the most powerful dark wizards known in that time.
The 'Greater Good' was a philosophy adopted by Dumbledore which stated that sacrifices have to be made when more people get something than lose something. Dumbledore lived by this and performed many other important but lesser deeds.
Voldemort feared Dumbledore probably because he knew his past. Dumbledore knew everything about young Tom Riddle until he left school. Furthermore he knew that Dumbledore was a very powerful wizard and fearsome as a foe.
This is a supplementary for the accepted answer.
I wanted to post this as a comment to the accepted answer. But since my reputation doesn't allow me to, I'll post this as an answer instead.
So Basically -
There is an interesting question posted here on scifi.stackexchange:
The answer with the most votes on that question essentially answers your question. Check it out.