I would like to add a link on a field's "Field description" text-box of a certain section, which will pop-up a specific image.
I have created a link like
<a href="/image.jpeg" target=_blank>(Press here to see the image)</a>
but it obviously opens the image.jpeg in a new page, which is something I do not want.
It sounds like you want to have the image pop up as an overlay without leaving the page - is that correct? For that sort of effect, you'll need to use a 3rd-party lightbox or modal library. This is one that I've used a few times in the past that is fairly simple to set up: https://lokeshdhakar.com/projects/lightbox2/
Hope that gets you pointed in the right direction!