My friend who carried this bag had no idea what it meant - she just liked the bag. To me it was simply a further outbreak of the 360 plague that infects our world to very little marketing effect.
Whenever I see it, I am struck that while I know it's meant to indicate something like constant interaction, it primarily reminds me that 365 is a much better known number - and thus 360 seems like taking 5 or 6 days off. It seems to be a diminished claim.
It's all very well for marketers to think they understand what 360 means in their world, but that's not enough to justify pasting it everywhere regardless of the sub-context, under the assumption that your customers understand it and in the misguided belief that it will aid differentiation. That way leads to things like Vodafone360 People.
Vodafone 360 People "brings all your friends together backed up in one place" which I'm not sure has much at all to do with the generally agreed 360 ideal. It strikes me that it's simply been bundled under the heading of Vodafone 360 that they advertise heavily in stores and brochures. It's the branding equivalent of scrambling around for some copy to fill the media space you belatedly realise you've bought. To confuse things further, they also promote Vodafone 340 in the same places. And no, that's not 360-lite. It's simply a phone.
I'm all for marketing making the meme, but when the meme's making the marketing, you've got problems.