You can change what is seen on a link in Facebook by changing the name of the item.
Keep in mind this change will also be seen on your website and can't be limited to Facebook only.
You can do this on the item by changing the Name (title) and Summary (short description shown under the title).
If you want to share the link to a page, like the home page, you have a bit more flexibility with changing the meta description and title. You can change the page SEO information by scrolling down just below the page editor and adding a Title and Meta Description of choice.
We would suggest keeping your meta description to about 150-180 characters or 2 lines because this is all that will show in a Google search for example and you don't want the information to be cut off.