The description of an image, shared with the button of Easy Social Share Buttons from any site, can be easily customized. The only detail you need to pay attention for to make your customization work flawlessly is the way you Pinterest button works.
There are different options need to be done if your Pinterest button is set to pin any image (Pinterest Marklet) or if you have disabled that option and prefer to share custom image.
Pin any image active
That is the default setting for Pinterest button. That option will provide your users the opportunity to choose what image from all the images on the page to pin on the network.
With that feature active the description is generated from the alt text description under WordPress Media Library. So if you use that pin method, to customize the share description you need to edit WordPress alt text of each sharable image.
Pinterest sniff for images disabled
When Pinterest Sniff for images is disabled, button pins featured image of the post or the custom image set under Social Share Buttons: Share customization -> Custom Pinterest Image. And the description is the title of the post.
If you want to change the description with Disable Pinterest Pin any image, use Customize Share Message (Advanced) option.
You will find it at Edit mode of each post under the post content part.