Paid in arrears means you are paying for a period of time that has already past. The subject as it relates to property taxes usually comes up when we explain tax prorations.
At closing, the settlement agent will calculate what taxes have been paid by the seller as of that date, then work out credits and/or debits between buyer and seller so that both have paid their fair share as of the date of closing.
Today is December 2nd. If I were prorating the school taxes on a parcel of ground in western PA, I would have the buyer reimburse the seller from today thru June 30, 2008. That is because the fiscal school tax year runs from July 1st thru June 30rd. The tax bills come out at the end of the summer and so often sellers and buyers think we should prorate as of the tax bill due date. We prorate on the fiscal year, whatever that is.
I like to use the analogy of the federal income tax. Though your payment to the IRS is due by April 15th of 2008, you are actually paying and reporting on taxes for the prior year.
I hope this answers your question. If not, please ask again but give me the context of the question.