The IP address that your home or business router receives from your ISP is a public IP address. Other devices on the Internet like the servers that host websites and the other network hardware involved in managing Internet traffic also use public IP addresses.
Devices with public IP addresses can communicate with other devices with public IP addresses but not directly with devices with private IP addresses. A router is required for public and private networks to exchange information.
Any IP address inside of a home or business network, like the IP address assigned to one of your personal computers, is a private IP address, not a public IP address.