Tags are key words add information about the item being tagged. Tags add semantic information about something in an effort to further it.
For instance, A picture of your father on his birthday could be tagged 'dad','family','event','birthday' etc...
By adding tags to the picture you add context and make the image more easily indexable, sortable and searchable.
Tags are purposely generic and flexible because different people can place different personal meaning to the same artifact, or the same person may apply different meaning in different contexts - like adding the same picture to a stock photography web site or checking it into a source code repository as part of a project.
Generally the procedure is to ask the owner of the item to add a list of tags in a text field. Some sites like stackoverflow constrain (most) users to use existing tags, others like delicious make the tags up to the user.