This is because your Google Wallet app is married to the secure element with a unique crypto key when you first set up Google Wallet on your phone and if you wipe your phone without first resetting Google Wallet, that key will be lost forever, rendering the secure element useless.
Performing a Google Wallet reset will unmarry the app from the secure element and reset it to its original state so that it can accept a new Google Wallet installation when you wipe your phone and then restore it to stock.
I had to get a new Note 2 because of this, thankfully I had phone insurance. If mods could sticky this, it would be great!
Google "secure element has stopped responding" if you don't believe me.
Engadget article explaining the problem: http://www.engadget.com/2012/05/29/g...reset-problem/
Android Community article on the issue: http://androidcommunity.com/more-goo...vice-20120529/
Phandroid article explaining the problem: http://phandroid.com/2012/05/28/andr...ak-it-forever/
A PSA thread on XDA warning of the issue: http://forum.xda-developers.com/show...php?p=26587822
Another XDA thread where Google and the Money Network both say you need a new phone if this happens: http://forum.xda-developers.com/show....php?t=1472117
Yet another XDA thread where someone bricked their phone: http://forum.xda-developers.com/show....php?t=1721222
For the naysayers, just because you've never seen something happen, doesn't mean it's not true or it will never happen to you. I just bricked my Note 2 and had to get it replaced under phone insurance. Went from the NoWiz ROM to MA7 stock rooted, wiped the phone in the process (my guess is Wallet stores the crypto key in /.android.secure, which gets wiped when you do a factory reset), installed Wallet on the clean MA7 ROM and got the dreaded "The secure element has stopped responding E00" error. NOTHING could make it reset. At all.
Also, to those who say Wallet stores things in the cloud now - false. Wallet stores its very own virtual card number in the secure element, which is what gets transmitted via NFC when you touch your phone to the reader. That number is then linked in the cloud to your actual credit cards, so your actual card numbers are not transmitted to the retailer. If Wallet stored nothing on the phone, it simply wouldn't work, period. Also, if Wallet stored nothing in the secure element, then it would work without it and not throw the "secure element not responding" errors, so it definitely stores something there, which is why it's important you don't brick it!