A private IP address is used as an unique identifier that your router assigns to each device found on your network. This allows information to be passed to specific devices accurately. Private IP address may also be refered to as an internal, network, LAN or local IP address.
A public IP address is assigned by your ISP (Internet Service Provider). This IP address is used to identify your network on the internet and is critical for running an email server, opening ports, or setting up a remote connection. May also be referred to as an external, WAN, or internet IP adresss
Your private IP address is critical when trying to communicate with devices across your network. Many networked software programs will store a database on a server and then connect from another device by using the private IP address. Some routers assign IP addresses dynamically and can change periodically. It can be advantageous to setup static IP addresses to prevent this.