During the lectures you have been told about Class A, B, and C IP-numbers. That's - however - not the whole story by far. There are two further Classes - D and E - as well as several special cases. You don't need to know that much about Class C and D as well as most of the special cases other than that they excist and where to get further infomation about these.
On the other hand, several of the special cases are very important in daily use.
127.0.0.1 is called the loopback or localhost address. This IP-number defines your own computer. Even though it might not even be connected to any network, it'll still have this IP-number defined and available. 127.0.0.1 is used for accessing services internally on your own computer. Servers and services on you own computer communicate with each other by using this IP-number.
Three special ranges of IP-numbers - one for each of the Classes A, B, and C - excist that are only ever used on a LAN. The ranges in question are:
This solves part of the problem with the limited number of available IPv4 addresses. For instance, a firm that uses eg. the Class A 10.x.x.x range of IP-numbers on the LAN is able to access the internet through a single IPv4 number common for the whole LAN. Thus, every globally available IPv4 number is theoretically able to point to a whole Class A subnet in the 10.x.x.x range greatly multiplying the number of computers it's possible to interconnect.
Another purpose in using these sub-ranges on a LAN is to isolate the LAN from the internet proper.
There's a problem with IPv4: the World is running out of available numbers. Even though there's 232 possible addresses we are fast running out of available numbers. The problem has it's root in the fact that the inventors of the internet simply didn't foresee the widespread use of computers and the need for interconnecting these. To solve this problem IPv6 has been invented. The available address space in IPv6 is 2128. At present IPv6 isn't widely deployed.