(from the book Baseball Prospectus, by Clay Davenport)
"Peripheral Earned Run Average (PERA) is the ERA you would expect from a pitcher who gave up this many hits, home runs, and walks in this many innings; it is essentially the equivalent average, calculated from the known pitching components (H, HR, BB) and assuming more or less average values for the rest."
PERA is a good indicator of next year's ERA when compared to this year's ERA; meaning if a pitcher's PERA is better than the actual ERA, then there is a good chance his ERA will be better next year. The converse of this is also true.
As an example: Mark Portugal had an ERA of 4.44 in 1998 for Philadelphia, and a PERA of 4.92. This would seem to predict that his ERA would go up, as the PERA was higher than the ERA. In 1999, Mark Portugal's ERA went up to 5.51 (though by using park-adjusted figures, his 1998 ERA was 4.60 and his 1999 ERA was 4.83, but this still shows an increase).