In an IPv4 class subnet mask configuration each octet will have a value of either 255 or 0. What does this identify, what does it mean and how is it used by routing components?

In an IPv4 classless (CIDR) subnet configuration one octet is likely to have a value other than 255 or 0. Include a mask configuration other than 255.255.240.0 and explain what that is identifying. How many bits are being used to identify each aspect of the IP address and how many hosts can there be on that network. Do not repeat a configuration that was previously described in this thread