The Pilgrim's Bounty holiday was introduced to World of Warcraft just last year, so it's still fairly new. This year, the event will run from Sunday, November 21st through Saturday, November 27th. On my EST server, the start and end times on both dates will be 4:00 am, but you'll want to check the times on your own realm.
Pilgrim's Bounty is not part of the yearlong meta What A Long, Strange Trip It's Been. That's not to say that the holiday's without its share of rewards, though; doing the Pilgrim meta will grant both the Pilgrim title and the plump turkey pet. However, the holiday has an unbeatable side benefit; it's the fastest, easiest, and cheapest way to level cooking to 350. Pilgrim's Bounty is tailor-made for anyone who needs to level cooking on a bunch of alts, or anyone who never got around to doing it on his/her main.
Pilgrim's Bounty hasn't appeared at any point on WoW's PTR or beta since last year, so we're assuming for the moment that the holiday hasn't changed from its 2009 incarnation beyond a few bug fixes (that and the developers are probably working at breakneck speed on Cataclysm still). I've updated and clarified our 2009 guide past the cut, and will also be around as the event goes live to ensure all the information here is accurate.