Home page show last post submitted

I want to develop my WP home page. However, When I publish a post, the last post always displays on the home page. I want it display under the category/subcategory. I have noticed that the check box is not checked where it says display on Home. How can I fix this problem. I have been trying to solve this problem for several days now and would appreciate any assistance.

site is still under development – blog URL is:
http://articleworld-usa/BLOG/