That is a
2D bar code. They hold keys or identifying bits of information (data) which in turn reference some other (normally more detailed) bits of information (held in databases). Just like the regular 1D bar codes, only holding more data in the pattern.
A mobile phone can be used to take a photo of the bar code, as published in various forms (e.g. websites). The phone can then be used to display the bar code to a reader at some other location. One simple example that comes to mind is a magazine advert for a event. If the advert includes a bar code it can be captured on a phone and then used later (at a ticket office) to automatically select the advertised event, ready for payment by card (no other human involvement). I imagine you can also buy tickets online and get a bar code as a proof of purchase, which is saved to the phone again to allow you into the event. I've not seen such systems used by the general public outside Japan, though I'm sure there are some.
Edit: Having just scanned the WikiPedia article, I realise I forgot to mention the possibility of the camera actually understanding (decoding) the bar code. This would allow the phone, if it can contact a website or remote server somewhere, to get more information about the item the bar code is on. More useful for adverts in trains and such, where a person passing might look, be interested, and take a photo for more information.