WPS (Wi-Fi Protected Setup) is a feature allowing devices to more easily connect to Wi-Fi access points without the need to provide a password or passphrase.
One common way that WPS is implemented is by access points and devices featuring a WPS "Push button" - this may be a physical button, as commonly seen on an access point, or a software button, as seen in Android. 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.
This effectively allows you to "pair" a device to an access point using a mechanism similar to Bluetooth pairing - being able to press a button on both devices is reasonable proof that the device user is authorized to connect to the access point, and in the event that someone else manages to connect within that short time window you'll know about it pretty quickly.
Occasionally, a Wi-Fi access point may support this feature but not have a physical push button on the outside of the device, instead having a virtual button that needs to be activated inside the access point's administration interface. 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.
It has become apparent that WPS has security weaknesses, and as a result it is not a good idea for it to be enabled in access points while it's not being used
Specifically, it is the WPS Pin Entry feature on access points that have been found to be vulnerable, rather than the Push button functionality. However, some access points may not allow you to disable their WPS Pin Entry feature without disabling WPS Push button as well.
The WPS PIN Entry feature is an alternative to a push button, supported by some access points.