WPS or Wi-Fi Protected Setup is a fairly secure way of connecting to a Wi-Fi network without having to enter a long, convoluted password. Although not as secure as a WPA or WPA2 connection, it is still a feature on most home Wi-Fi routers.
If you have chosen to connect to your Wi-Fi network using WPS, your Android phone has the option to allow this. Most phones have the option to connect using the WPS Push and WPS PIN method.
To find these options, you will normally need to enter the Wi-Fi connection screen on your phone, tap the menu button and select the WPS option you want to use from the menu that appears. You will need to turn Wi-Fi on before you can select an option.