Featured images are shown by default on the homepage, blog page, categories and search results. If you don’t have a featured image then you will see a placeholder. You also have the option in the Customizer to display the featured image at the top of of your posts and pages.
To add a featured image use the ‘Featured Image’ function in the right hand column of the post/page editor:
To show the featured image at the top of your posts and pages go to Dashboard > Appearance > Customize > Site Options: