What it is: We normally think of scoring purely in totals, i.e. Teemu Selanne scored 26 goals and added 40 assists for a total of 66 points. Advanced stats simply extrapolate the numbers over 60 minutes played. The purpose is to eliminate differences in opportunity by brining the numbers to an even number for comparison. In other words, it makes sense that guys on top lines outscore guys on bottom lines because they have more playing time to score. Calculating stats in this way allows us to see how well a player is using his time rather than simply calculating totals that can be greatly biased towards players who get more time. This is a calculation that can be used for any statistic, such as hits, blocked shots, giveaways, etc. For example, Devante Smith-Pelly's leads the team in hits/60 this year at 15.16, If I did the math right. Currently, scoring is the only one behindthenet.ca is using it for.
Limits: It can't account for diminishing returns. Yes, all these guys are athletes, but around 18+ minutes, you might not be getting the same output as you would in earlier minutes.
Advantages: It allows us to compare players who receive unequal minutes to see who is making the most of their time on ice. That can be used to make arguments as to why some players might deserve to be moved up or down the lineup.
What it means: The scoring/60 stat is a wonderful tool for getting passed the low totals of players who get less ice time, and is good for evaluating streaky players. It gets the stats to the purest totals. The stat literally tells us what we should be able to expect from a player every 60 minutes played. However, this is a stat that is best used very early in evaluation or at the end of the season. Early in the year we can see hot hands by looking at the p/60. However, as things settle in towards the middle, the stat can become inflated by early success. It can be seen as a trend statistic, but I think it's better to be seen from the holistic view of the season.