Significance:
Apple going out of business, er? Presumably just like the doomsayers have been saying for the past 20 years or so?
Once upon a time...
There was a time, particularly around the mid-1990s, when Apple's future looked bleak. After a series of bad decisions, an unclear direction, so-so products, and Microsoft having its golden era, Apple were haemorrhaging market share, market value, and customers. Apple's name could not be uttered without the word "Beleaguered" being attached, and everyone in the computer industry expected Apple to go the way of all the other non-Microsoft affiliated PC manufacturers, such as Commodore, Atari, and Acorn.
But they didn't. They weathered the storm, and not only pulled though, but with their co-founder Steve Jobs back at the helm, they went on to diversify and grow into one of the healthiest companies in Silicon Valley.
Granted, things can change. Apple's fortunes could degrade in the future, or indeed go on to be even more successful. But unfortunately, the crystal ball isn't that specific.
That ye olde market share argument
Hovering at around the substantially-sub-10% market share (exact number depending on which way you look at it) may not sound too impressive, and indeed wouldn't be if computer sales worldwide ran into the mere hundreds; but that percentage of hundreds of million of units sold per annum, is hardly small fry.
As a platform, sub-10% puts the Mac at a very distant 2nd place behind the Microsoft steamroller. But that level of sales also puts Apple in, or close to being in the top 5 biggest shifters of PCs in the world, with only Dell and Hewlett-Packard currently well out of reach. That's a position most other PC manufacturers would be envious of. And is particularly impressive when you consider they don't even make any models that you could particularly call 'budget'.
See also reason 33
'Macs have got a tiny market share'.
Profitability
And of course, all that is just in terms of number of boxes shifted. That's not even looking at their profitability and overall market value. From that perspective thanks in no small part to the highly successful diversification into digital music and movies via iTunes, iPod, AppleTV, and iPhone Apple are profitable, solvent, they sell everything they can make, and are worth more as a company than many of their competitors who sell many more boxes than they do.
If this is the definition of a company in the process of going to the wall, then I'd like to be this unsuccessful!
'Apple computers: Proudly going out of business since 1984'