A cookie is a small bit of information which is kept on your computer. It is typically used to ensure the functionality of a web site, but it can also be used to collect statistical information on a user's activities in a web site.
The cookie law was created to protect users from the unsolicited collection of user activity statistics. All Danish websites are required to inform its users about the cookies which are placed on the user's computer. The information must be in accordance with Danish law which is in turn in accordance with EU's "Directive on Privacy and Electronic Communications".
You can in all normal browsers choose to disable cookies. Note that this can mean that certain web sites no longer function correctly. Read more about your options at your chosen browser provider.