In Facebook speak an Edge is a piece of content - a status, a picture, a like, even a relationship status change. The precise algorithm is secret, but it's reckoned that the EdgeRank is made up of three factors -
Affinity - how well you know someone, based on how frequently you interact with them
Weight - how engaging the content is in their post - it's thought that photos, videos and links are given the highest weights
Recency - how recent the content is
Each is given a score, and when you log in your news feed is made up of items that have the highest combined scores (e.g. 5 x 2 x 3 = 30 would beat 3 x 3 x 3 = 27)
The next question is what you can do to increase your EdgeRank...
One of the most important things is to increase your affinity - that is, how often people interact with you.
Here's a classic example. Whether accidentally or by design, Snoop Dogg has come up with the idea of Puff Puff Pass Tuesday, and yesterday asked his Fans (of which there are more than 10m) to tell him what they were smoking...
So far there have been over 10,000 'Likes' and nearly 2,500 comments... It's a great way to engage the fans, particularly for Snoop, and it will almost guarantee that all of those people seen the next few things Snoop posts.