Here is a section from a Cisco class I am taking (note the bolded text near the end).
Historic Network Classes
Historically, RFC1700 grouped the unicast ranges into specific sizes called class A, class B, and class C addresses. It also defined class D (multicast) and class E (experimental) addresses, as previously presented.
The unicast address classes A, B, and C defined specifically-sized networks as well as specific address blocks for these networks, as shown in the figure. A company or organization was assigned an entire class A, class B, or class C address block. This use of address space is referred to as classful addressing.
Class A Blocks
A class A address block was designed to support extremely large networks with more than 16 million host addresses. Class A IPv4 addresses used a fixed /8 prefix with the first octet to indicate the network address. The remaining three octets were used for host addresses.
To reserve address space for the remaining address classes, all class A addresses required that the most significant bit of the high-order octet be a zero. This meant that there were only 128 possible class A networks, 0.0.0.0 /8 to 127.0.0.0 /8, before taking out the reserved address blocks. Even though the class A addresses reserved one-half of the address space, because of their limit of 128 networks, they could only be allocated to approximately 120 companies or organizations.
Class B Blocks
Class B address space was designed to support the needs of moderate to large size networks with more than 65,000 hosts. A class B IP address used the two high-order octets to indicate the network address. The other two octets specified host addresses. As with class A, address space for the remaining address classes needed to be reserved.
For class B addresses, the most significant two bits of the high-order octet were 10. This restricted the address block for class B to 126.96.36.199 /16 to 188.8.131.52 /16. Class B had slightly more efficient allocation of addresses than class A because it equally divided 25% of the total IPv4 address space among approximately 16,000 networks.
Class C Blocks
The class C address space was the most commonly available of the historic address classes. This address space was intended to provide addresses for small networks with a maximum of 254 hosts.
Class C address blocks used a /24 prefix. This meant that a class C network used only the last octet as host addresses with the three high-order octets used to indicate the network address.
Class C address blocks set aside address space for class D (multicast) and class E (experimental) by using a fixed value of 110 for the three most significant bits of the high-order octet. This restricted the address block for class C to 192.0.0.0 /16 to 184.108.40.206 /16. Although it occupied only 12.5% of the total IPv4 address space, it could provide addresses to 2 million networks.
Limits to the Class-based System
Not all organizations' requirements fit well into one of these three classes. Classful allocation of address space often wasted many addresses, which exhausted the availability of IPv4 addresses. For example, a company that had a network with 260 hosts would need to be given a class B address with more than 65,000 addresses.
Even though this classful system was all but abandoned in the late 1990s, you will see remnants of it in networks today. For example, when you assign an IPv4 address to a computer, the operating system examines the address being assigned to determine if this address is a class A, class B, or class C. The operating system then assumes the prefix used by that class and makes the appropriate subnet mask assignment.
Another example is the assumption of the mask by some routing protocols. When some routing protocols receive an advertised route, it may assume the prefix length based on the class of the address.
The system that we currently use is referred to as classless addressing. With the classless system, address blocks appropriate to the number of hosts are assigned to companies or organizations without regard to the unicast class.