When you start a company, you choose a "tax year" by filing a tax return. From then on out, you file your tax return the same month every year.
If it's a small business, you probably find it most convenient to have the tax year be the calendar year and match up with your personal filing.
Many businesses have some concept of a "selling season" that makes it really convenient to not use January through December. A retailer, for example, probably prefers not to close their books on December 31 every year because of all the post-Christmas gift returns. Walmart has a January fiscal year (February 1 through Jan 31).
If you sold stuff to schools, you might choose a June fiscal year; most universities use a June fiscal year so an entire school year stays in a single fiscal year.
I have no idea why Apple chose September, but it was probably a rational decision.
For a variety of reasons, some public companies will use a non-standard or non-calendar quarterly reporting system. For example, Walmart's first quarter is February, March, and April; Apple Inc's Q1 is October, November, and December; Microsoft Corporation's Q1 is July, August, and September.
In addition, certain governments use different quarter systems. The first quarter of the United States federal government’s fiscal year is October, November, and December, Q2 is January, February, and March, Q3 is April, May, and June, and Q4 is July, August, and September. State governments may also have their own fiscal calendars.
Sometimes a company may have a non-standard fiscal year to help with business or tax planning. The Internal Revenue Service (IRS) allows companies to choose a “tax year” that is still 52-53 weeks long but does not end in December. H&R Block (HRB) ends its fiscal year on April 30th, which makes sense because that is the end of the busiest part of the company’s year. Releasing your annual report, which may be accompanied by shareholder meetings and additional disclosures after the busiest part of your year will help managers and shareholders make better decisions about the year ahead.
Companies that rely on U.S. government contracts may use September as the end of their fiscal year, and the fourth quarter because that is when they expect new projects to be closed and budget planning from the government to be available. Historically, large technology firms had stronger quarters early in the year, which is why many of them (including Microsoft (MSFT)) have a fiscal year that closes at the end of June.
Some companies have very unusual quarterly systems. Adobe (ADBE) closes their fiscal year on the Friday closest to November 30th. In 2018, November 30th was a Friday, as well as the last day of the month but in 2017, ADBE closed their fourth quarter and the fiscal year on Friday, December 1st, because it was the Friday closest to November 30th.
> Some companies have very unusual quarterly systems
This can make things quite confusing when comparing revenue or earnings between periods as years may have 52 or 53 weeks (a 2% difference) and quarters may have 12 or 13 weeks (a 8% difference).
It's because Apple has to account for returns, and their biggest quarter is the December quarter. Most retail companies do not end on Dec 31 for this reason.
There's a slight tax disadvantage in using a non-calendar fiscal year since tax brackets typically adjust upwards annually and the non-calendar accounting means that you'll be booking some revenue in year X at the less advantageous year X-1 tax rates. But other accounting matters can outweigh that.
Along other reasons, with such a massive percentage of their income (and income variability) in Q4, it really helps their accountants to close out a tax year in the (relatively) predictable and stable Sept after three quarters of normalizing cashflows.
Sheltering taxes in a double-Irish requires pretty accurate projections.
Also often they just don't have all the data they need to close out a year until a few weeks after holidays, especially if people are taking a break, so it's just a lot easier on the humans involved.