In a private key, all users must have access or be given a secret password or group of words. This information is used by all sides for data transmission. DES is used by most governments and larger computer systems such as Unix servers. The obviously problems with this type of key is that once you know the key, is hard to remove the privilege. Changing the key for large groups of users can be a nightmare for any IS department.
Public keys are a little easier to use.
This process involves both a public key and a private key, also called a secret key. The public key is just that - you publish this key or post it on the Internet where anyone can find it. Your secret key is kept private so only you know. When you wish to send someone some personal information like your credit card number, you encrypt this information using your secret key and the public key you published on the Internet. In easy terms, the data is mixed or changed with a stream of other data based on the key codes.