I have found that it stands for Wireless Protection Setup.
I think it has to do with being an option for connecting to a router that has the same "WPS" button setup feature. Its basically a simplified router connection setup.
Wi-Fi Protected Setup (WPS) is a standard for easy and secure wireless network set up and connections. WPS lets you use push buttons or PINS instead of entering a network name (SSID) and wireless security by hand.
Yup, it is a simplified secure connection between device and router - I have an IP camera that I connected that way - you don't need to make a passphrase/keycode to connect and make your device secure, it does it for you automatically thru a push of a button on each device - it reacts in the same way and simuliar to how you pair a BT headset to your phone, i.e., a push of a button on both devices make a secure connection.
It won't be a physical button
I don't recall it being in the settings either. You will find it under the wireless settings. If it's there, it will probably just be the two arrows circling each other, with no words. If not, than you'll have to pair it up to the router the old fashioned way, by entering the passcode set in the router.