It's Classless Inter-Domain Routing (CIDR) . It tells the router how big the network is. This can be a complicated subject so I can't (more accurately won't) attempt to explain all of it here but if you're interested in learning more you need to do some research on subnetting and subnet masks.
Default subnet masks per classes are as follows.
Class A: 255.0.0.0
Class B: 255.255.0.0
Class C: 255.255.255.0
What this indicates is the number of bits allocated to hosts (computers/router ports/devices on your network/etc.) versus the number of network bits that designate the network portion of the address. This is why in most SOHO routers out of the box you will see a local (non internet routable, private) address of 192.168.1.x with x changing based on the device through DHCP. The 192.168.1 is the network portion and the .x is the host portion. Since you need to reserve a broadcast address and a network ID so that your router knows how to get to your local area network this gives you a total of 254 addresses that can be assigned to devices.
That's just default masking though, it waste a lot of address space if your network only needs 30 IP addresses. The /27 changes the mask from 255.255.255.0 to 255.255.255.224 which tells you that your range of addresses on the 192.168.1.0 network must increment by 32. Something like this.
192.168.1.0
192.168.1.32
192.168.1.64
etc.
So basically what it is trying to tell you is this. Let's use the NY1 router and the Host A machine. /27 there means that your network is identified as 192.168.1.32, your router then knows that this is the network and sends traffic there. The gateway for that network is 192.168.32.33 which is the first of the 30 available host addresses in this subnet. Ultimately it just means that that network can have addresses ranging from 192.168.1.33 - 192.168.1.62 . 192.168.1.32 is reserved for the network ID address, 192.168.1.64 is the next subnet, 192.168.1.63 is reserved as the broadcast address when using protocols such as ARP to identify devices on the network.
Feel free to PM me if you have further questions.
E; RIP is a protocol used for routing internal networks (non-internet, local area networks). The internet uses BGP.
This post was edited by Lethardus on Sep 2 2016 02:04pm