Hi nicholeclare.
Different WordPress themes display your post on the home page in different ways. Many times you can log into WordPress and head over to your theme’s settings and adjust how much of your post or how little you want to show on your home page.
When people click on the post title, they should be sent to the actual post where people can comment as well.
There are certain reasons why you might not want your entire post to show on your home page. Two such reasons would be duplicate content (nothing real bad but can hurt some in search engine rankings) and also making your home page really long with lots of words.
A home page is a great navigational page, so many people simply like to put snippets of their last 5-10 articles on there for people to preview and then click over to read more.
There is a plugin called Evermore which I like which will allow you to display more of your post on the home page if you like.
If you want to display the full content of each recent post on your home page, there should be a setting someone in WordPress, maybe under your theme’s settings, where you can change this option.