pIC50 is the negative of the log of the IC50, the way pH is the negative of the log of the H+ concentration. One advantage of using the log is to be able to conveniently compare numbers that differ by several orders of magnitude.
For example, suppose in your project you have inhibitors with IC50s of 100 µM (1 x 10-4 M) and 100 pM (1 x 10-10 M), which is a likely scenario. Database programs typically require you to use the same units for all the values, such as µM or M. In that case, the database would show the two values as 100 and 0.0001 µM, requiring you to carefully count all the zeroes after the decimal point. You might find it easier to view the pIC50s as 4 and 10 (in log molar units).
Another nice aspect of pIC50s is that more potent compounds have higher numbers instead of lower ones.
You can also graph the pIC50s on linear axes when creating an SAR plot, instead of using logarithmic axes for the IC50s.
I think it is a matter of taste which measurement you use. Why not put both values as columns in your database, and use whichever one seems most convenient for a particular purpose?
The pIC50 is not really a new approach for expressing potencies of inhibitors, but I believe that it has some advantages over the IC50, as Dr. Shapiro has pointed out.
There is an excellent blog post on this issue called "Why using pIC50 instead of IC50 will change your life."