A number of people have already pointed out that a corporate fiscal quarter doesn't necessarily align with the calendar year. There are assorted benefits to this, usually around the seasonality of income. Some companies with multiple sub-corporations may choose to have differing fiscal years for all the corporations which can somehow create a tax advantage (although beats me how that works). It's interesting to note also that there's a (smallish) tax disadvantage to not aligning with the calendar year in that typically tax brackets adjust upward from year to year and having a non-calendar fiscal year means that income might be taxed at a slightly higher rate since the tax rate is based on the year the fiscal calendar begins. At large corporation scale, this difference amounts to a rounding error.
Apple's fiscal year (internal accounting year) ends Sept, 30th instead of being aligned with the calendar year.
This is very common for companies with holiday-linked or time-linked sales. It's much easier to make your big chunk of sales in Q1 (October-December for Apple), then have the rest of your fiscal year to spend that money. Getting all your revenue in Q4 is much harder to budget around.
BTW it is not 'exactly' September 30, it is usually last Saturday in September. So it does not even align at a 'calendar month' boundary.
In addition to what others have said, a ton of companies don't even align their fiscal quarters with calendar quarters. This is especially widespread in the SaaS sector, where companies normally go Feb 1 - April 30, May 1 - July 31 and so on.