An IP address (Internet Protocol address) is a unique identifier for each connection to the internet. Its primary purpose is to allow devices to communicate with each other. IP addresses are somewhat analgous to a postal address.
IPs are commonly described as an identifier for each internet-connected computer but this is not entirely accurate. In a common household setup, you may have multiple computers, phones, tablets, etc connected to a single internet connection through a router (or combination of routers). In such a scenario, all these devices would have the same public IP Address. In the case that your cell phone is connected to the internet through a wireless carrier, your cell phone would have a different ip address than your computer that is connected through your local ISP.