What is Link Juice?
Link juice is a phrase which a lot of online marketers use to describe the beneficial effects which a link from one site passes on to the site which its link is pointing toward. Link building is still one of the best things which you can do off site to improve your rankings in the search engines, so working to secure links from high ranking websites will go a long way to boost your visibility in the SERPs.
Link juice can never be precisely or accurately quantified but it's understood that some links bear a great deal more link juice than others. For example, an established authoritative site which has been around for awhile and has a number of good links pointing to it itself will pass on a great deal more link juice than from a relatively new site.
It should also be mentioned that not all links pass on link juice from one site to another. A link is either DoFollow or NoFollow, meaning that it either passes on link juice or it doesn't.
If you want to link to another site but don't want to pass any link juice to that site, you would use a NoFollow tag with that link to notify Google that you don't want to pass on any influence. It's still a live link, meaning people can click through to get to that site, but again it simply won't pass on any influence which only the search engines are concerned with.
As an example, leaving a comment on someone's blog used to be a great way to get a link back to your site from theirs. Of course that method got abused which is why most links generated from comments nowadays are NoFollow style by default through content management softwares like WordPress.
This is in an effort to weed out the SEOers who only leave spammy comments for the express purpose of getting a link and encouraging the idea that the only people leaving comments for NoFollow links are doing so because they have something to add to the discussion.