Every device connected to a computer network is assigned a number (an IP address) so that other devices can identify it. This is true for your internal network (your computers/phones and router) and also for the internet, where your router or computer is assigned a publicly visible IP address. The most common method of assigning IP addresses is dynamically (this is called DHCP), which means that they are automatically assigned and rotated among a given pool of users.
This works great when you are connecting to outside servers from your home, as outside servers don’t usually care what IP address you’re coming from. Since dynamically assigned IP addresses can change frequently, there can be problems if you need to connect a server that requires a pre-approved IP address, or if you need to connect to your home computer from somewhere else (though there are now many cloud services which provide this functionality).
This is where a static IP address can help. Rather than belonging to a large group of randomly assigned IP addresses, a static IP address is assigned to one specific user, and only changes if that user requests a change. Static IP addresses are primarily utilized by business and remote workers, but have many possible applications for tinkerers and tech enthusiasts.