From the Hockey Reference site:
Expected GF/GA and +/-
While Corsi and Fenwick count shot attempts, they don't account for quality of the shot. Expected +/- considers the shot location, and uses league-wide averages to determine the likelihood of that shot being a goal. It doesn't factor in whether the shot actually resulted in a goal or not. Instead, it's giving a sense of shot quality by looking at the odds of scoring a goal from that location.
A team which has an Actual Goal Differential exceeding its Expected Goal Differential ('axDiff') indicates a team converting or stopping an inordinate amount of good chances compared to league average. This could indicate the team has great shooters, a prolific goalie, or is just getting lucky.
A negative differential would indicate a team is getting more good chances than its opponent, but is not converting or is allowing more than league norms. This could mean bad shooting, bad goaltending, or just being unlucky.
Scoring Chances and High-Danger Scoring Chances
As originally defined by War On Ice, 'Scoring Chances' indicate shots attempts that are taken from areas of the ice where goals are more likely to be scored. Attempts made from the attacking team's neutral or defensive zones are excluded.
Inside the zone, a shot is assigned a value of 1,2 or 3, depending on where it was from. A rebound shot (defined as any attempt made within 3 seconds of another blocked, missed or saved attempt without a stoppage in play in between) adds a point to this value. A blocked shot decreases the value by 1.
'Scoring Chances' are any shot attempts with a final value of 2 or higher. 'High-Danger Scoring Chances' are any shot attempt with a final value of 3 or higher.
Explanation of advanced hockey stats like Corsi and Fenwick
www.hockey-reference.com
Still pretty subjective and cloaked in a certain level of mystery, but that's the basics of it.