There are a number of ways to do this. Perhaps most common is the full size image is contained in a modal. The linked demo opens a small text message on button click, but the same concept can be applied to a thumbnail image that opens a modal that covers the entire viewport.
There are a number of JavaScript libraries available to make development easier. For example Lightbox is one of the originals in this vein. This is not a WP plugin though, you need to be able to integrate it into your own bespoke plugin. There are however a number of Lightbox-like plugins. Using an existing plugin is the easiest way to accomplish what you’re after.
