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Private IP address of a system is the IP address which is used to communicate within the same network. Using private IP data or information can be sent or received within the same network.
Public IP address of a system is the IP address which is used to communicate outside the network. Public IP address is basically assigned by the ISP (Internet Service Provider).
To check if your IP address is public, you can use myip.com (or any similar service). You will be shown the IP address of the sender of request to the site; and if it matches the IP address that your Internet service provider assigned you (i.e the one that is shown on Dashboard's infopanel), then you are assigned with a public IP address.