What is link juice and why should I care?

The SEO term 'link juice' refers to the search engine 'trust' (i.e. credibility) and/or page rank conveyed by a link from one site to another. A site with high 'trust' or page rank provides more link juice than one that doesn't.

For example, a link from a popular Wikipedia page provides more link juice than a link from a brand new site. Why? Because Wikipedia has a lot of trust and high pagerank in the search engines (especially Google).

In SEO (as I write this), the aim is to secure inbound contextual links from external sites that have established search engine Trust and high page rank. This transfers some of that trust and page rank to the site being linked to.

SEO guys call this 'link juice'.