What do the different formats for network addresses indicate?

I've seen the following forms for network addresses:

• 10.1.1.0
• 172.16.1.0
• 192.168.1.0

I usually see 192.168.1.0 for my home network address. Sometimes I've seen the other two forms listed above. What do setups with the other two network addresses indicate?

All of these are private network IP adresses, the last one is typically used for home networks, but as it offers the smallest number of sub-adresses, the other ones might be preferred for larger networks like e.g. company intranet.

IP address range              number of addresses   classful description
10.0.0.0 – 10.255.255.255     16,777,216            single class A
172.16.0.0 – 172.31.255.255   1,048,576             16 contiguous class Bs
192.168.0.0 – 192.168.255.255 65,536                256 contiguous class Cs

All 3 designate private non routeable IP addresses.

With IP addresses you must be assigned one by the managing authority, unless you use a non routable address. What that means if your address is in

10.x.x.x
192.168.x.x
172.16.x.x – 172.31.x.x

when your request goes to a router that bridges your network and the internet the request can not cross the router. What will happen because you can not use that private IP on a public network is at the router it will do something like Network Address Translation (NAT) and it will use the single IP it was given by the ISP and map the internal IP addresses to that single public IP.

Nothing. See RFC 1918

The Internet Assigned Numbers Authority (IANA) has reserved the following three blocks of the IP address space for private internets:

 10.0.0.0        -   10.255.255.255  (10/8 prefix)
 172.16.0.0      -   172.31.255.255  (172.16/12 prefix)
 192.168.0.0     -   192.168.255.255 (192.168/16 prefix)

We will refer to the first block as "24-bit block", the second as "20-bit block", and to the third as "16-bit" block. Note that (in pre-CIDR notation) the first block is nothing but a single class A network number, while the second block is a set of 16 contiguous class B network numbers, and third block is a set of 256 contiguous class C network numbers.

An enterprise that decides to use IP addresses out of the address space defined in this document can do so without any coordination with IANA or an Internet registry. The address space can thus be used by many enterprises. Addresses within this private address space will only be unique within the enterprise, or the set of enterprises which choose to cooperate over this space so they may communicate with each other in their own private internet.

These are defined in RFC 1918 as private (aka non-routable) IPv4 addresses.

• The 10.0.0.0 – 10.255.255.255 range if a single class A address space.
• The 172.16.0.0 – 172.31.255.255 range is 16 separate class B address spaces.
• The 192.168.0.0 – 192.168.255.255 range is 256 separare class C address spaces.

They're class A, B & C private networks

class A 10.0.0.0 – 10.255.255.255 have a subnet mask of 255.0.0.0 and support 16,777,214 hosts

Class B 172.16.0.0 – 172.31.255.255 have a subnet mask of 255.255.0.0 and support 65,534 hosts

Class C 192.168.0.0 – 192.168.255.255 have a subnet mask of 255.255.255.0 and support 254 hosts

As you can see Class C is the most suitable for a home network, in fact its suitable for most networks, as a good network architect should be able to split the network up to sections so that the broadcasts don't slow down the network.