These are to represent the heroism aspect of the game. Edge Points (EP) allow PC's (and even some NPC's!) to affect the fate of their character. Each character starts with 2 Edge Points and gains an additional one for every 20 Experience Point. (Should a GM want, they can get rid of Edge Points for a gritty campaign, or give them out more frequently - such as 1 for every 10 XP - for a more Heroic or Cinematic campaign.)
Examples of Edge Point use are as follows:
1) Re-roll the dice by using one Edge Point: Of great use when that telling shot to the evil ringleader just misses... or failing the Dexterity check to avoid falling into the Lake of Fire while jumping from pillar to pillar...
2) Locate a contact: Janelle and her posse are trying to track down the location of a suspected fraudulent banker responsible for stealing thousands of cred from her employer. The players however, have run up against a wall and don’t know how to proceed. Janelle's player decides to use an Edge Point to “remember” her good friend happens to work at Trans-travel, and can provide information about the last Void Jump ticket that the suspect purchased.
3) Find Equipment: The battle is going badly for the PC's, two of their number are down and Grevan is trapped in a Tangler grenade's sticky threads. His player spends an EP to remember that he had forgotten to take out the spare bottle of solvaway from his vest pocket that's just in reach.