i'm definitely no networking expert but this is how things work from my understanding.
first you need a modem that connects to your isp which connects you to the world wide web, this modem will be issued an ip address from the isp, either static or random, from their issue of available ip addresses..
now most home modems have a router and switch built into them today so unlike in days gone past you can connect more than 1 device at a time to the internet. ie. a network of devices. (we're just going to call this device a router from now on.)
your router is your gateway to the internet and usually has a local network ip address of either 192.168.x.x or 10.0.x.x you can set the x.x to anything you like but i understand the first 2 sets of numbers need to stay the same depending on your router. (i'm going to assume from now on the main router address is 192.168.0.1)
now the router also uses a subnet mask address usually 255.255.255.0 to identify and communicate to any device connected to it.
this subnet address is used to create a sub network of devices on your 192.168.0.1 network, for most home networks we always use the same 255.255.255.0 so all devices can see and talk to each other if required, but for some work situations you need some devices to be hidden from others on the same network, to do this they use a different subnet mask number, eg 255.255.255.100
now all devices use the 192.168.0.1 as the gateway and all devices using 255.255.255.0 subnet can be seen and talk to each other and all 255.255.255.100 devices can be seen and talk to each other yet they can't see or talk to devices in the other subnet mask group even though they are all on the same main 192.168.0.1 network. ie. they are a sub network.
regardless of the subnet mask every device will be issued (or have manually set a static ip address) a unique address in the range of 192.168.0.x where x is anything from 2 to 255 every time it connects to the router using dchp .
now when you add a second router, you are in effect creating a 2nd totally separate network but the same rules apply to this network and subnet as the original network router if you have it set as a dchp server, but because the first router is using 192.168.0.1 the second router will always need use a different gateway/network address, eg. 192.168.1.1
networks can be very complicated setups, and not being an expert in the area this is just my basic understanding (and may not be 100% correct.) of how they work.
hope that explanation helps a little anyway.
Edited by terry1966, 07 August 2016 - 02:55 PM.