The Basics of Categories and Tags
A category is a helpful way to organize or group your posts in a thoughtful way. They are generally used as a way to group post topics on a broader level (than tags for example).
Depending on the theme and widgets chosen, categories can be used to display posts from a specific group or displayed in a list format for navigational purposes.
Posts can also be assigned more than one category, where the categories can then be organized hierarchically. Note: A post must be attached to at least one Category. WordPress will automatically file new posts in a “Uncategorized” Category if you do not create one.
Examples of some categories might be: News, Videos, Reviews, or Photography.
For more information on categories, please visit the WordPress Codex
A tag is similar to a category but within a smaller scope. Tags are used to describe all or part of a post. It’s also a great way for the reader to learn what the post is about. A post may have several tags, relating to various parts of the post, however they are not required.
Depending on the theme and active widgets, tags can be displayed in clouds making it easier for readers to navigate to a topic of their choice and learn what the posts are often about.
Examples of tags might be: iPhone 5s, Sony, digital camera, or architecture.
For more information on tags, please visit the WordPress Codex