Well, VLAN's are really used to create a virtual network between computers that are not on the same network/subnet/etc. Think of it like a VPN (Virtual Private Network).
Network Segment 1 has Computer 1/2/3/4
Network Segment 2 has Computer 5/6/7/8
Each network segment is isolated by a router/private WAN, etc. These networks cannot talk to each other because they are protected by the WAN firewall (unless other wise specified like port forwarding)
Say Computer 1 and Computer 5 are both Corporate Accounting and need to access the Accounting server on Segment 2. A Virtual LAN will then be created between them by designating certain ports on the Switch/Router denoting them VLAN1 instead of the default VLAN0 (or however your network devices specify the VLANS). This then isolates their communication and will pass information back and forth. Even though they are on different physical networks, they are on the same logical network.
Since you're setting up 3 routers, you'll be creating 3 network segments. This is done in larger corps to stop collisions and broadcasts as well cut down on the amount of traffic through the backbone.
Of course security comes into play too because if Network 1 is compromised, then Network 2/3 are still okay because they are segmented off.
Your routers SHOULD stop all attempts to access computers from other networks by default, just like it does right now from the Internet (This wasn't a request sent out, I have no ports to forward to for incoming therefore no soup for you). You can always set up specific ACL's (Access Control Lists) to explicitly deny access from those routers too.
