Taxonomy is basically about creating tags or categories for EACH content page or node.

Wikipedia's definition of folksonomy most aptly describes Drupal's definition of taxonomy.

Example if we are running a simple magazine with 3 sections say Sports, Economics and Politics, we:-

Select Administer > Content Management > Categories > Add Vocabulary > [Title] Topics > Submit >.....
> Add Item > [Title] Sports
> Add Item > [Title] Economics
> Add Item > [Title] Politics

Drupal will create a dropdown 'Topics' list for each content type we define eg. page, story, book, etc

So when say we create 6 content of 'page' type, we tag (categorise) each page either into sports, economics or politics accordingly.

Perhaps a grave-to-cradle approach helps in understanding.

This is a site built with Drupal. This page displays all those nodes that contain both the categories (or term) 'Argentina' AND 'banknote' together. We are able to do this because for each node (content page) we tagged them accordingly.

Taxonomy is thus a very easy to understand concept and in Drupal, it is easy to create and apply. Though simple as it is, Drupal's power in taxonomy is amazing; there are so many different types of content eg. page, story, blog, image, etc and for EACH content type, we can tag it. We can create many tags like main topics with sub-topics... the combination is incredible....
..... AND we can grant (or refuse to grant) access/permission to say only certain type (user role) of users for certain topics only... example if a user (say 'sports_user)subscribes for sports section, then he can only access those content tagged as 'sports' only. Go to Drupal's website, look for and download the (external) contributed module called taxonomy_access module.