When you list articles in a category, you often end up with some order which you didn't want to have. By default Joomla displays articles in the "Latest First" order. So newer articles will go to the top and older articles will go to the bottom of the page. While this is a good ordering for websites related to news and likewise, it may not be suitable if you want a specific order for your articles.
To order the articles manually, go to Article Manager. In the category drop down, select a category to order Articles inside that category. Now click on the column heading named "Ordering". Now Joomla will sort the articles in the current order. See below screen shot
Now to change this order, you can either type in numbers in to this textbox or you can click the "blue arrow" to move the article up or down. After completing the ordering, click on the "Save" button (Near the heading "Ordering") to save the ordering.
Now to make sure that Joomla displays articles in this order, go to "Menu Manager" and click on the menu item which displays articles from this category. On the right side you can see "List Layouts > Article Order". From the drop down select "Article Manager Order". Now save and go to your website, you can see articles listed in the order you want them to be.