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In my mobile I see three sections under Wi-fi settings
1. turn-on wifi
2. Setup Wi-fi network
3. Wi-fi networks
I want to know about what the second option do? Under that section I see Auto setup(WPS). What does it do? When I click on this option it gives a pop-up asking to "press the wps button on a WPS compatible access point".
Please explain what does it do?
Loosely translated it means you need a pin number instead of a security key - Every 24 hours or however many hours you set your router too it will change the encryption key but if you use a pin your devices will auto update with this new encryption key,
Mainly used in cafes etc every day they will give the new encryption key say to there customers and then the next day it will change but if the owners use a pin then they don't need to constantly update there wireless settings and or key
Your answer tells that it is not useful for home networks? home devices? like laptop and mobiles
WPS, as far as I know, is a once off setup.
Traditionally, to connect to a secure network, you need to key in a password for the wireless network.
With WPS, all you have to do is press a button on the WiFi router (if it supports WPS), and the WPS button on your WiFi device or the button in the settings like you've seen in your phone.
You could use it for a home network if your devices are compatible with this feature,
If they are compatible and you live in fear of someone been able to hack your wireless encryption key everyday or whenever they feel like doing so then it can be a good thing.
Should I buy external device for this feature to work in Xperia S?
I am asking this question because I see this message when I click on that option in mobile "press the wps button on a WPS compatible access point".
Thanks I got it. See now everything is in Wireless then why this feature is provided 
Phones will have this option because alot of people use this feature for example as I mentioned above ie: Cafes etc If you are the owner would you want to constantly update your phones wi-fi settings or have your phone auto update with the new encryption details
Nice Nice thanks lot ... can you please look at this post as well and reply if you have answer Create Wifi connection in Xperia S to use internet