Link Juice - Use 1
Link juice refers to the the link value a link is able to pass on to the target.
This could be power and link trust, and any other aspects helpful for improving organic rankings, e.g. anchor text relevance.
Link Juice is often used as a simplification of a much more underlying system to evaluate links. In absence of knowledge or name for accurate metrics for a link SEOs often use it there to differentiate between weak and strong links.
This link seems to pass a lot of link juice, pushed me to page 1 over night right after I got it.
This term link juice has been used since the early 2000s and stuck around in blogs, forums and social media.
Some people in the SEO industry mention they dislike the term "link juice", often because of the vague (no) definition of it.
LRT recommends to always refer to the Power and Trust of a link instead.
Link Juice - Use 2
The Bulk URL Analyzer of LRT was also named "Link Juice Tool" in the early versions.
Link Juice - Use 3
Some companies created all sorts of swag (conference giveaways) around "Link Juice". Often this was a white-labelled energy drink.
However, link juice was never meant to be consumed by SEOs, but by websites.
For ecological reasons, LRT doesn't approve of production and shipping of heavy CO2 loaded and waste-generating marketing material like energy drinks.