Organising your articles using Joomla categories can help organize content for front-end users and for yourself in the back-end. Here's some of the ways having a good category structure can help you and your visitors.
Create a Blog
Let's say you have a website for your brick and morter business to help get your name out there. On this site you might have one category "Business pages" and another category "Blog".
Each business page, such as your home page, about, contact us, photo gallery, faq, testimonials, etc, would have it's own menu link. But you also want a blog for your website, to share special sales you're going to have and other news about your business. You don't want to link to each of these "posts" from your menu or it would get too big. Rather, you show them all in a blog format. You have one menu link to "the blog".
The Joomla blog works by taking all articles in a category that you choose (in this case, the category you have named "Blog"), and showing them in a standard blog layout with the teaser intro followed by a "read more" link to the full article.
The second most important part of making a website, after providing quality content, is to make it easy for your visitors to use the site. If you have a series of articles that relate to each other and should be read in a particular order, you might like to use the "Previous" and "Next" buttons.
These buttons will take you through each article in a category, so for each set of article you have you will need to create a new category, otherwise these navigations buttons will take your readers through to unrelated articles.
An alternative, if you want to break down a very long article into multiple pages is to use "Pagebreaks".
They are also useful for finding your content. If you are just looking for an article to update, having them in categories can help narrow down what you are looking for.
Also very important, categories help you find an article when linking. Linking to an article in Joomla is a whole can of worms but as mentioned (in the linked article), the JCE extension helps you link properly. But first you need to find the article.
Alternative to Categories
One downside to categories is that you can only include an article in a single category. Your bike website has two categories, bikes and bike accessories.
You can nest categories, meaning the bike category could be a parent category for road bikes, tandem bikes, and bmx bikes. Any road bike articles can be shown alongside bike articles.
But you can only put an article in one category. Because bike and bike accessories are sibling categories, your article about tandem bike chains can only be included in one and will not simultaneously show up in the "bike" blog and the "accessories" blog, should you want it to.
The alternative, since Joomla 3.0, is tags.
You can apply multiple tags to each article. If you list articles by tags, you can show articles in multiple places. However, the category blog layout vs the tag list layout is currently different and the tag list doesn't include any "read more" links.