When you create a WordPress post you have the option to assign categories and tags to that post.
Categories are hierarchical groupings, whereas, tags are not hierarchical.
In other words, your categories can have parent categories and children categories (or subcategories). This helps to organize your content for menus and other hierarchical charts/pages. This allows you to break categories of posts into smaller sub-categories.
Tags, on the other hand, do NOT allow you to have sub-tags. They just allow you to indicate which topics your post is about.
You can have multiple categories and multiple tags for each post.
Both categories and tags will create archive pages out of the box, meaning a page for each category and task will be created which lists all the posts assigned a certain category or tag. This is a great way to create pages for your menus without much extra work. It will automatically group your posts for you.
I've heard arguments from SEO 'experts' that say tags are not good for SEO purposes, but my philosophy is to make my blog/site good for my audience and forget about SEO. If it's truly good for my audience, then SEO will 'catch up' eventually. The SEO algorithms are changed often to benefit the reader, not the SEO expert.
However, don't create so many tags that it does water down your site. Remember that search engines, and your visitors, will get an idea about what your site, as a whole, is about by the pages you have on your site. If you have too many categories and tags it will be overwhelming to both the reader and the search engine, and they won't get a good picture of what your site is truly about. The more focused your site can be on one main topic, the better it will land in the search engine rankings, and the easier your visitor will be able to find you and appreciate your content.
To see a category archive page, use a link similar to this: http://your-site.com/category/category-slug
For instance, the link to the 'Web Development' category on my blog would be: http://cullenwebservices.com/category/web-development/
Tags are similar. The link to my tag archive for the 'child theme' tag would be: http://cullenwebservices.com/tag/child-theme/
Use your tags and categories wisely to organize your website in the best possible way for your readers. Help them find what they are looking for. Everyone, including the search engines, will love you for it!