WordPress says this about tags:
“Refers to micro-categories for your blog, similar to including index entries for a page. Posts with similar tags are linked together when a user clicks one of the tags. Tags have to be enabled with the right code in your theme for them to appear in your post.”
Tags thus provide a useful way to group related posts together. It allows your readers to quickly tell what a post (content) is about and find similar posts. Tags are similar to, but more specific than categories. The use of tags is completely optional.
You can add an unlimited number of “Tags” (or keywords) as sub-organizing topics. I describe “Tags” as being folders within the filing cabinet drawer, or articles within a folder. Or think of them as the Dewey decimal system used to organize books within a library’s sections. One WordPress video refers to theme as the ingredients (tag) in recipe (category) in a newspaper’s food section (post page of the Web site).
This WordPress support article on Tags includes a good video.
Also read about the difference between categories and tags on this WordPress page.
The next section talks about Widgets in Posts.