Link juice is a jargon term used in the field of search engine optimization to describe the complex value search engines give to linked web sites when determining page rank.
When determining the ranking of a site in a search results list, most search engines will take into account the quantity of other sites that link to it. The reasoning here is that if a site is creating interesting, desirable content, then people will recognize this and send others there. Since people are better than web crawlers at determining the quality of a site, many search engines weight this factor very heavily.
The first thing determining the amount of link juice a site has is simply the quantity of unique sites that link to it. More sites means more juice, which means a higher results rank.
Additionally, search engines take into account the reputation of the linking sites. A web site that has a large amount of traffic and a high ranking of its own, such as a news site or a popular blog, will create more link juice than a rarely visited site. If that site has a lot of link juice of its own, created by other sites that link to it, some of that will trickle down to the sites it links.
Finally, link juice can also be increased if the linking sites are similar in content and format to the linked site.
Since link juice is a slang term, it is rarely referenced directly by search engine companies. However, a good explanation can be found at http://thekeywordacademy.com/link-juice-explained
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