The Dumbledores are a prominent Wizarding family who lived in Mould-on-the-Wold until an attack by Muggle boys on the youngest child, Ariana, left her disabled. Ariana’s father, Percival, defended his daughter against the Muggle attack and was subsequently sentenced to Azkaban. The rest of the family then moved to Godric’s Hollow and lived there until another terrible accident resulted in the death of Ariana, then 14, and her mother, Kendra. Both of the older sons, Albus and Aberforth, were haunted by these tragedies all their lives.
“Dumbledore” 18thC Eng. word for ‘bumblebee.’ Rowling says she wanted to associate his name with bees because she imagines him wandering around the castle humming to himself.
In a 5 November 2000 interview on BBC Radio 4 with Sue Lawley (DID), J K Rowling said that "Dumbledore came straight out of Thomas Hardy. Dumbledore is used in The Mayor of Casterbridge as a dialect word meaning “bumblebee” - and I loved that word."
Interestingly, the word "dumbledore" has another possibly important meaning. In an e-mail, Christopher Woosley writes:
"Although not widely known, an alternate meaning for the word Dumbledore is a style of hat the was made semi-popular in London in the 1880s-1890s. Taking this meaning into account, Albus Dumbledore's name would have the meaning "White Hat." As I'm sure you know that is a term for the hero or protagonist of a story. Mrs. Rowling named her great champion of good "White Hat"...I ran across this alternate meaning while researching a paper on British literature of the 19th century."