Hi there,
That device will connect to the wifi of your existing router and allow users to connect through it. It appears to boost the signal but it depends on the signal between it and the router, which might be weak anyway.
You can connect any router to any of your ethernet ports but will require a small configuration change.
At the moment you have a router connected to the internet which is acting as a gateway. A gateway is responsible for handing out IP addresses to connected devices like PC's/phones etc and there can be only one per network.
If you connect a second router, it will also try and act as a gateway and give out IP's which will conflict and cause your network to stop working.
So the second router needs to have it's gateway features disabled.
First thing to do it configure the second router to have a different IP from everything else on the network., but within the same range as the first router.
For example, if the first router's IP was 192.168.1.254 then manually set the second router to 192.168.1.253. If you add a 3rd router then have it as 192.168.1.252 and so on.
After the IP has been set then disable the DHCP service, which is probably on the same page you used to change the IP.
That's it. Fix an IP and disable DHCP.
You should now be able to connect to either of the wifi's and get internet.
Thanks