What does “192.168.1.1/21” mean?

Question

When they write a slash followed by a number after an IP address, what does that mean?

Answer 1

The part after the slash is how many subnet mask bits to use. Since the use of classless routing you use slash instead of saying class A or B whatever. Example:

192.168.1.1/24 is 192.168.1.1 255.255.255.0

255.255.255.0 is using 24 of the 32 bits to create the subnet.

in binary it looks like this:

11111111.11111111.11111111.00000000

so a /30 would look like:

255.255.255.252 or in binary 
11111111.11111111.11111111.11111100

the remaing 00 is for hosts; the 1's are the network.

Answer 2

It's CIDR notation for a subnet.

The /21 denotes that the first (most-significant) 21 bits are common to all addresses in the subnet. The individual hosts in the network have addresses that are different only in the last 11 bits.