A server outage at Apple disrupted Wi-Fi connections for many—possibly all—iOS device owners who had upgraded to iOS 6. The issue effectively knocked users off of whatever local Wi-Fi network they were on and kept them from logging back on to that network or on to a new network.
The issue stems from a check within iOS that checks to see if a user is on a network with a pay or Term & Conditions wall. Apple's iOS devices check the Success page on Apple's servers (that's our name for it). If the device gets through, the page returns "Success," which iOS reads without displaying it, and your device goes on its merry way.
If not, iOS knows you're behind a wall, which is how iOS knows to show that popup window for, say, a Starbucks network that requires you to sign off on the T&C before surfing.
What happened on Wednesday was that the Success page stopped working and returned this page, instead:
Analyst Michael Gartenberg Tweeted this Screenshot During the Outage
iOS didn't know how to handle that error page, so it kicked device owners off the local Wi-Fi network. That had the side effect of sending all Web traffic through your cellular connection, which had the practical effect of many people not even realizing anything had changed.
Now that it's over, look for some questions to be asked about how Apple will prevent this from happening in the future.