The purpose of a taxonomy is to provide more granular searching and grouping mechanisms for your sites content. Both categories and tags work in similar ways with a couple key differences between them.
A category supports hierarchy while a tag does not. This means that tags are independent from each other and are not related in anyway. Categories by contrast can be setup with another category serving as it’s parent. This is especially helpful when you have a lot of content and need to breakdown the details into very granular sub-categories. For more information visit the Category definition.