CIDR, or Classless Inter-Domain Routing is a new IP allocation scheme that is intended to replace the class-based allocation system.
Class-based allocation system includes three classes, each with a set maximum number of host identifiers:
Class A - 16+ million identifiers.
Class B - 65,535 identifiers.
Class C - 254 identifiers.
Now, supposing that you need 1,000 host identifiers, you would no longer fall into Class C (as you've gone above the maximum 254 identifiers). Instead, you would fall into Class B, despite the fact that you are way below the 65,535 identifiers.
As you can see, this method greatly limits the availability of IPv4 addresses.
What CIDR does is define prefixes of arbitrary lengths. CIDR addresses are written as 190.255.255.255/16. The first part (190.255.255.255) is a prefix, just like for a class-based IP address. The second part (/16) servers as a suffix and shows the number of bits in that address.
This Variable-Length Subnet Masking (VLSM) makes CIDR a much more effective IP allocation system.