Reading an address
To get messages, a device on a network needs an address, like a house needs one for post. Your laptop's IPv4 address here is 192.168.1.20.
An IPv4 address is four numbers with dots between them: 192, 168, 1, 20. This style is called dotted decimal. Each number can be anything from 0 to 255.
A bit is a single 0 or 1. Each of the four numbers is stored as 8 bits, called an octet (or byte). Eight bits make 256 patterns, which is why the numbers run from 0 to 255.
Each of the 8 places is worth a value: 128, 64, 32, 16, 8, 4, 2, 1. Put a 1 in the places that add up to the number: 128 + 64 = 192. So 192 is 11000000.
Do the same for the rest: 168 = 128 + 32 + 8, 20 = 16 + 4, and 1 is just the last place. Four octets of 8 bits make 32 bits. Computers only use the bits; the dots are for people.
Network and host
The first part of an address names the network; the rest names one device on it. Here /24 (the prefix length) says the first 24 bits, 192.168.1, are the network and the last 8 bits, 20, are the host.
Think of the network part as a street and the host part as a house number. A message for 192.168.1.20 goes down street 192.168.1 to house 20. The router lives at house 1.
Special ranges
Three ranges are private (RFC 1918): 10.0.0.0/8, 172.16.0.0/12, 192.168.0.0/16. Millions of homes reuse them, so they work only inside a network, never out on the internet.
Addresses from 127.0.0.0 to 127.255.255.255 are loopback: they mean this very device. A message to 127.0.0.1 never leaves your laptop. Programmers use it to test things.
On its internet side your router has a public address, here 203.0.113.5. Public addresses are handed out so that each one belongs to just one network in the whole world.
32 bits give 2^32 = 4,294,967,296 addresses, and some are reserved. That is fewer than the devices online today. NAT (sharing one public address) and IPv6 (much longer addresses) solve this; both come later.
The numbers, worked out
device your laptop IPv4 address 192.168.1.20 written as dotted decimal (four numbers, three dots)
192.168.1.20, 192.168.1.1 and 192.168.1.35 are private RFC 1918 addresses; 203.0.113.5 is an RFC 5737 documentation address standing in for a real public one. Prefix lengths do not have to fall between the dots (for example /20); the subnets lesson shows how that works.