The display and size of this image depends on the theme. Most themes will crop and resize it to fit properly on the site.
The theme can create several variations of the image for display in different contexts. For example, the blog page may use the front page image in a square shape while the post may display it in other proportions.
It is in the editing interface of a post or a page that you can associate a featured image with your posts. Usually, a link is located at the bottom of the right column.