All of the above answers are great, but are missing something pretty important for the people who don't understand addressing.
IP addresses are literally just a string of binary, broken up into 4 "octets". Each octet is a 2^8 block; 00000000. So to a machine, an IP address looks like this (with (.) added for human-ness):
00000000(.)00000000(.)00000000(.)00000000
When we're talking about the "mask" on the IP address, it means "the bits that don't change". The /8 or /255.0.0.0 on the end of the block signifies the number of bits that are not allowed to be used by this network.
So, lets say we have a CIDR block of 10.0.0.0/8 - this can also be written in the format 10.0.0.0/255.0.0.0, and you may in fact see this for of notation in older versions of linux. You will also note that 255 is the decimal representation of the binary string 11111111 - 8 binary "ones". So what the machine sees is the following:
Net: 00001010(.)00000000(.)00000000(.)00000000
Mask: 11111111(.)00000000(.)00000000(.)00000000
The part of the mask with 0's is usable address space within the network.
So the following example addresses are valid in this network, because on the 0 parts of the masked range are changing:
00001010(.)00000001(.)00110000(.)00111000
00001010(.)00110001(.)00110100(.)00111001
When we say "cidr block" we simply mean "the human-readable shorthand way of expressing binary strings understood by a machine". In the above example, the first octet can be expressed as 10, and the latter octets 0. And the Mask can be expressed as 255 and the latter octets of 0, or; because the mask is always a sequence of 1's, then a sequence of 0's, the length of the 1's, i.e. 8
And as such, we get a cidr of 10.0.0.0/255.0.0.0, or 10.0.0.0/8
A few more examples:
-- 172.1.1.0/24
net: 10101100.00000001.00000001.00000000
mask: 11111111.11111111.11111111.00000000
^ 24 bits for the mask ^ 8 bits of usable space
-- 10.10.10.8/29
net: 00001010.00001010.00001010.00001000
mask: 11111111.11111111.11111111.11111000
^ 29 bits for the mask. ^ 3 bits of usable space
Importantly though, this is only one aspect of networking. Usually a couple of these are reserved for things. See other answers for AWS specific things. In their examples, the "first 4" ip addresses reserved for AWS will be the first 4 usable addresses, which would be
...00 - Network address
...01 - Router
...10 - DNS
...11 - Futureproofing