There is no such thing as an "accrual year."  You are thinking about a FISCAL year, which is an accounting year that starts on any date other than January 1st.  The most commonly used dates to start Fiscal Years are October 1st and July 1st of the preceding year; my company's fiscal year 2010 starts on October 1st 2009.

A company which is uses Calendar Year accounting opens its books on January 1st and closes them on December 31st.

An "accrual-basis" company is following GAAP.  They recognize income when they record accounts receivable, and they recognize expenses when they record accounts payable. 

The alternative is a "cash-basis" company which doesn't recognize income until cash is received, and doesn't recognize expenses until cash is paid.  Most US Income Tax law is built around "cash-basis" accounting.

So, an Accrual-basis, Calendar-year company is one which uses GAAP accounting and measures its year from January 1st through December 31st.