Categories are subjects that a group of blog posts share. Pages do not have categories, only posts. Categories, like pages, can have a parent category, which creates a category hierarchy. Managing your categories can be done from your Wordpress dashboard under Posts>Categories. After your categories are established you can simply select the category your post pertains to while editing your post.

One example of category usage would be a car manual; Categories would be engine, brakes, cooling system, etc. All blog posts pertaining to its category would be selected. You can have more than one category selected.

Tags are also for posts, not pages, which are more specific topics within a category. Tags are added to a post in the edit post screen.

Using the same car manual example, a tag would be brake fluid, coolant, spark plugs; all topics within a category.