He provides a better technical explanation than I ever could but in layman's terms what he did is create a league table based on expectations and reality. What this means is that not all points are created equal. The top six is expected to get three points at home v Wigan, so those three points don't actually count.
Think of it as golf. Three points v Wigan at home is expected, so if we win, it's only a par (anything but a win gives us negative points). Getting three points from United away, on the other hand, counts as a +3 because par (or the expected points) for United away is 0. Instead of arbitrarily deciding who's points are worth more, they've used math to do it thus eliminating subjectivity.
So what does this mean for Chelsea? Well, despite being fourth on the actual table, we're third on their table with +14.71. City are +17.07 and Spurs are +13.16. Arsenal are 5 points behind with +9.26 and Pool..... well, who cares about Pool. Both tables eventually become the same thing at the end of the season.
I might've simplified it a bit too much but I hope you find it as awesome as I did.
Edit: Here's the summary he wrote: "The concept is simple. Each team plays the same fixtures [over] the course of a season but they don't play them in the same order, which means the table will be misleading as some teams have played a harder set of matches at each point in the table. This adjusts for that."