Are you referring to a particular settings? Those names of feat types are not core but are often used in campaign settings sourcebooks (although it's also possible that some 3ed supplement attempted at giving them a more general definition), so you should check what they really mean in your setting.
If you're trying to look for a more general definition, the typical idea behind them is fairly simple, and you can guess it from their names...
Ancestor feats are used to represent a talent or potential that runs in your family's blood. Taking the feats means such talent has manifested in your character; whether this came out spontaneously or you trained to discover it, and whether it manifested gradually or was triggered by some event can be left to RP and description, or otherwise can be dictated by the campaign settings' specific take on ancestor feats.
Normally the point of ancestor feats is to be available only to characters who belong to a certain family, clan, or even race as a whole (although then they would be more likely call "racial feats"), and as such are used by the campaign setting to (a) give something more in common to every character belonging to the same clan/race and (b) differentiate between characters of different clans/races. However it is possible that a DM just gives ancestor feats more freely and then justify this by saying that the character simply discovers to be the descendant of such ancestor.
Regional feats serve pretty much the same purposes, but are instead thematically explained in terms of the character being born and raised in a specific region and therefore having been exposed to a certain culture and education. A regional feat usually represents then some superior expertise or easier approach at something that is more common/valued in such culture.
The standard is to require characters to have one and only region of origin, which gives access to a series of regional feats (and possibly something else) to choose from if you want your character to emphasize her cultural roots. An alternative approach could be to instead allow regional feats based on the time spent in such regions, thus also allowing a PC to get regional feats of different regions at different times, provided that this is backed-up somewhat by what happens in the story.
(edit) Also note that some published settings effectively use the term "regional feats" to include "racial feats" as well, to emphasize that they are more about cultures than actual geographical areas. So a character in such setting may choose "Elf" or "Dwarf" as "region", provided of course her actual race matches (or the DM has allowed concepts such as "being raised by elves").
Background feats, I actually don't know if such thing exists explicitly in published settings... to me usually "background feats" is rather a term used for any feats that the player gives her character to represent something she's learned either before being and adventurer or during her downtime off adventuring, and therefore most of the times such feats would be of the kind that don't help in action: for example, skill-related feats, item creation feats, or any feat that is related to the interaction phase.
I have actually heard some DM using house rules where feats that are recognized to be background feats (also in the sense that the DM identifies them being significantly less useful for the game itself) are made cheaper, e.g. getting two background feats in place of one regular useful feat.