"You know how my poor father sought revenge, and paid the price, died in Azkaban."
-- Albus Dumbledore (DH35)
Percival Dumbledore was the father of Albus, Aberforth, and Ariana Dumbledore. When Ariana was attacked by three muggle boys, Percival went after them in “a savage and well-publicized attack.” (DH2) He was convicted and sent to Azkaban in 1891, where he would later die. (DH2) Neither Percival nor his family ever revealed the reason he attacked those muggles, in a bid to protect Ariana. His actions, believed to be an act of prejudice against muggles, were a stain on the Dumbledore family’s reputation until eclipsed by Albus’s academic achievements. However, his name never was publicly exonerated.
"Percival" was one of the King Arthur's Knights of the Round Table. Percival was an honorable knight, which alludes to Percival Dumbledore not being a simple muggle-hater and acting out of love for his daughter. Percival passed his name down to his son Albus.
Prior to the publication of Deathly Hallows, it was assumed that the name Percival indicated the goodness of Percy Weasley and/or Albus Dumbledore, but it turned out to be most indicative of Albus's father.
"Dumbledore" is an eighteenth-century English word for "bumblebee," which has more bearing on Albus than Percival.