What does closing month of accounting year mean . Trying to obtain a EIN number to establish Mom's estate account

If your accounting year is the same as the calendar year, the closing month is December.   If it is not, the closing month is the 12th month of that year.   A bank officer helping you open an account for the estate should go online to www.irs.gov while you are sitting with her and get an EIN for the estate.  It literally takes two minutes.