Long story short? The subnet mask determines which numbers can change. A mask of 255 means there is no change. A mask of 0 means any number can change. So for instance, a range of 192.168.1.0 with a mask of 255.255.255.0 will only find other devices in the 192.168.1.x range. Because the last octet is the only one that isn’t 255.

And writing the range as 192.168.1.0/24 is simply a shorter way to accomplish the same thing. Each group of numbers is an octet made of 8 bits. So masking the first 8 bits (255.0.0.0) is /8. Masking the first 16 bits (255.255.0.0) is /16, and masking the first 24 bits (255.255.255.0) is /24. So 192.168.1.0/16 would be able to find anything in the 192.168.x.x range.

If you want to get really deep in it, you can manually calculate subnet masks. Remember that computers work in binary, and the octets are each a group of 8 bits. For example, the IP address 192.168.42.67 could also be written as 00000011.00010101.01010100.11000010 but that’s a nightmare for humans to remember so we use base 10 by default.

The subnet mask tells the computer which bits may be different. So a subnet mask of 255.255.255.0 looks like this: 11111111.11111111.11111111.00000000. So the computer will only scan for neighbors on any bits that are 0’s (unmasked). So in this case, if the range is 192.168.42.0/24, it will assume that the first three octets (192, 168, and 42, respectively) are going to match. So it will only scan for differences in the last octet.