Which button are you referring to exactly? If you mean the one on the front, under all the lights, it's the WPS button (Wi-Fi Protected Setup).
You only need to use button if you want to connect a WPS-capable device to your Wi-Fi. Instead of using the Wi-Fi password, you can press the button so that it can connect.
For more info you'd need to look into it specifically with the device you are trying to connect to see if it's capable of being connected via WPS.
Hope that helps