Link juice is a colloquial term in the SEO world that refers to the power or equity passed to a site via links from external or internal sources. This power is interpreted as a vote of recommendation toward your site and is one of the most important factors in determining your site's search ranking (and PageRank).
While I realize your post is copied and pasted from someplace else - Page rank is no longer updated in the public view and PR never did mean very much to begin with.
PR is not in any way one of the most important factors in search rankings and never was. Quality content has always been the top ranking factor and always will be. Not backlinks, not link juice and certainly not spamming every social media site you can find - It's quality content!
One of the biggest, missed opportunities I see in SEO is wasted link juice. SEOs and link builders alike are in relentless pursuit of high value links and the equity and semantic relevance that those coveted links carry. However, the irony is they often overlook vast, untapped reservoirs of concentrated link juice on the very Web properties these SEO link builders control: their own or their client's sites. So when I visit a site and see page after page of equity-rich pages that haven't been "milked" of their juice properly, I get a little glum .