It is actually the impact people and webmasters are expecting to gain after building links for their websites, traffic combined with improved ranks. Although even PR might be sometimes named as a juice passed to the links recipients, but positive impacts of the votes on domains stats could be their real strength.
Usually that is how some webmasters refer informally to Google PageRank. Every page has some value / authority in the eyes of Google, and by linking to other pages, it can pass some of that authority to them. How much authority your page receives from other pages through inbound links affects your keyword rankings. Keep in mind that it is only one of about 200 ranking factors, so while you should keep it in mind, you don't need to be obsessed with it. Build links to make people visit your pages, and PageRank juice will come along naturally.
Link juice is the currency of Google. In other words, it’s the secret sauce that allows you to beat your competitors for rankings in Google. Sure, there are some other factors that Google uses to calculate rankings, but link juice is by far the most important aspect of dominating Google and in order to understand Google, you have to understand link juice.
The term link juice is directly concerned in SEO, since this is the juice that will drive up your rankings and bring visitors to your websites..
Link juice explained (scroll up to section just above): http://www.squidoo.com/dofollow#module120875901