In Arizona, property taxes are paid bi-annually - the May payment covers the last half of the previous year. The October payment covers the first half of the current year. Let's say a purchase closes April 9, 2012. The seller would pay the last half of 2011 (the previous year) at closing, if it hadn't yet been paid. On the first page of the HUD-1, the seller will give the buyer a credit for the taxes from Jan 1, 2012 through the closing date, April 9, 2012. Then in October, 2012, when the buyer pays his first half taxes, he pays the full amount, but at the closing in April he received the seller's portion as a credit.
Hope that helps explain it. If you have any further questions, please don't hesitate to give me a call.