The menu system is a very important part of Joomla, and not just because every website needs a menu. With Joomla, the menu dictates the URL structure of each page and a tidy URL system is good for SEO.
Menu Link vs Blog
In Joomla, you can publish an article but that doesn't necessarily mean it will show up on your website. For it to show up and be accessible, it needs to be linked to.
The most direct way is to create a menu item link to that article (Menu Item Type > Articles > Single Article). (See this video tutorial on how to do that.) If you created an article "Joomla Rocks", created a menu item with the same name and didn't set a parent menu item, the URL would be yourdomain.com/joomla-rocks. (That's a nice simple URL!)
An indirect way to make an article show up on your site is with a category blog (Menu Item Type > Articles > Category Blog). Any article put in that category will show up in a blog format on that page. When you clicked on the article, the URL wouldn't be so clean. More like yourdomain.com/category/24-joomla-rocks.
Joomla is slowly getting better for now, you still need a menu strategy.
Joomla Menu Strategy for URL
Use the Blog
If you don't want to make a menu item for every article, this is for you. Just create a category blog menu item and publish your articles to that category.
It's not the best URL structure in terms of SEO but it's only one of many, many things google looks at. Everyone agrees what is most important is that what you write is quality and that people are reading then sharing.
However, if you have a cleaner URL, it can help with the sharing part.
Every Article a Menu Item
If you go this route, you have much better control over your URLs.
I call this the sitemap method because one way to do this is to create a single menu that links to every page on your website. If you do this, you can easily put that menu on a "Sitemap" page that lists every page on your website.
For navigational menus (the ones at the top of the page, footer menus, etc), use menu item alias links to will create a "copy" of the sitemap menu item (Menu Item Type > System Links > Menu Item Alias).
The sitemap strategy is great because at any time you can change main navigation menus without altering the URL structure. (If you change URLs, visitors can get lost. Lost visitors leave. Also, google will stop loving you.)
Does all this sound like a lot of work? You can save time making menu links using a RegularLabs.com extension called Add to Menu. I install it on every new Joomla project I do.
How do you control your Joomla URLs?