An IP address (Internet Protocol address) is a number assigned to every device connected to the internet. Just as a phone number lets people reach you by phone, an IP address lets other computers find and communicate with your device on the internet.
There are two versions of IP addresses in use today. IPv4 uses a format like 192.168.1.1 - four numbers separated by dots, each ranging from 0 to 255. This system can create about 4.3 billion unique addresses, which seemed like plenty when it was designed in the 1980s. However, as more devices connected to the internet, the available IPv4 addresses ran out. IPv6 was created to solve this shortage, using a longer format like 2001:0db8:85a3::8a2e:0370:7334 that can provide far more addresses than IPv4.
IP addresses are divided into two categories. A global (public) IP address is unique across the entire internet and identifies your network to the outside world. A private IP address is used only within a local network, such as your home Wi-Fi. When multiple devices connect to your home router, they each get a private IP address internally, but they all share a single global IP address when communicating with the internet. The router handles the translation between private and public addresses using a technique called NAT (Network Address Translation).
Some URL shortening services record the IP addresses of users who click on links. This data powers geographic analytics - since IP addresses can be mapped to approximate locations at the country or city level, services can report where clicks are coming from. However, an IP address alone typically cannot identify a specific individual.
Most home internet connections use dynamic IP addresses, meaning the address your ISP assigns can change each time you connect. Businesses and servers often use static (fixed) IP addresses that never change.