Simple,
Private IP Addresses are ones used within your local network and are usually non-routable IP addresses, which means you cannot use them on the Internet. You can choose the private IP address you wish to use.
A private IP address identifies your computer within your private network.
Public IP Addresses are assigned by your ISP and you usually cannot choose them. These IP addresses are routable and identify your pc or network to the Internet.
Cheers,
