You need to use Open Graph meta markup to have this type of sharing on Facebook .There are so many plugins available in the WordPress repository for this.
For example:
<meta property="og:url" content="http://sharing/url" />
<meta property="og:type" content="article" />
<meta property="og:title" content="Title of the post" />
<meta property="og:description" content="Description or excerpt of the post" />
<meta property="og:image" content="YOUR FEATURED IMAGE SOURCE" />
The above meta needs to be available for the post that is being shared based on this FB crawler get correct information as how to show your post.
You can also preview you post as how it looks for the FB crawler here.
References: