What's a Z-Score?
The z-score is a statistical measure of how a particular number compares to the average. Technically it is the number of standard deviations from the mean, but one need not have a complete mathematical understanding of the z-score to appreciate that it shows how a given player performs compared to the competition.

For example, if the league average for home runs is 9 and a player hits exactly 9 home runs, his z-score is zero. If he hits more than 9 HRs his z-score will be positive and if he hits fewer than 9 it will be negative. Precisely how positive and how negative will depend on how other players in the league fared. For example:

In the National League in 2001 the league average for home runs was about 12. The leaders:
Barry Bonds 73
Sammy Sosa 64
Luis Gonzalez 57
Several others also exceeded 40. Bonds' HR z-score was +5.20.
In the American League in 1920 the league average for home runs was about 4. The leaders:
Babe Ruth 54
George Sisler 19
Tilly Walker 19
Happy Felsch 17
Nobody else exceeded 12. Ruth hit nearly three times as many HRs as anyone else (in fact, he alone hit more than any team beside the Yankees), so his HR z-score was +8.45 which shows mathematically what we see intuitively: that his performance was more dominant than that of Bonds in 2001.