Networks and addresses
IP address
The number that identifies a device on the internet, in two versions: IPv4 (32-bit, scarce) and IPv6 (128-bit, plentiful).
Every packet on the internet carries a source and a destination address. IPv4 addresses are 32 bits, written as four numbers (31.24.249.1); there are about four billion and they ran out years ago. IPv6 addresses are 128 bits, written in hexadecimal groups (2a0e:...::1), and there are more than enough for everything.
A public address is routable on the internet and reachable from anywhere. A private address (10.x, 172.16–31.x, 192.168.x) is only valid inside a local network and is translated to a public one by NAT on the way out. Behind CGNAT even the router has no public address of its own.
Addresses are handed out by the regional registries to networks, not to people, and every block is registered with an abuse contact. A server comes with at least one public IPv4 address; IPv6 is usually a whole prefix.