WPS (Wi-Fi Protected Setup) is a feature allowing devices to more easily connect to Wi-Fi access points without typing in as much information.
One common way that WPS is implemented is by pushing a WPS "Push button" on both an access point and a device.
If you have access to your Wi-Fi access point and it supports this feature, you can push a specially-marked "WPS" button on your Wi-Fi access point or router, and within a short time also activate the WPS Push feature on your device, and the Wi-Fi connection should be established.
Alternately, it is possible that some Wi-Fi access points support this feature but do not have a dedicated physical button on the outside of the device, but instead have a virtual button that needs to be activated inside the settings of the access point. In this case, you will need to log in to your access point's settings, activate the WPS Push feature, and then within a short time activate the WPS Push feature on the device.
Evidence has emerged that WPS itself can be vulnerable to security weaknesses, and as a result it is often not a good idea for it to be enabled in access points, at least for long periods of time.
Specifically, it is the WPS Pin Entry feature on access points that have been found to be vulnerable. Some access points may not allow you to disable their WPS Pin Entry feature without disabling WPS completely, however.
Some WPS-enabled devices also support a WPS PIN method, which can be used with the WPS PIN Entry menu option in your Android device.