An accounting year is simply the 12 month period over which an organization’s accounts are calculated. Deciding what 12 month period you use depends a great deal on what makes the most sense for your organization.
Calendar year – A calendar tax year is 12 consecutive months beginning January 1 and ending December 31.
Fiscal year – A fiscal tax year is 12 consecutive months ending on the last day of any month except December. A 52-53-week tax year is a fiscal tax year that varies from 52 to 53 weeks but does not have to end on the last day of a month.
For more in depth information, take a look at the IRS Publication 538.