Product in Pivots, to my knowledge, is not regularly used. It may have been included for consistency's sake. This function is similar to the function in Excel =PRODUCT(range) that returns the numbers in the range multiplied together. If you have 3 in A2 and 2 in A3 and your function is =PRODUCT(A2:A3) it returns 6. The Product function works in PivotTables in the same way. It will return the results multiplied together.
The results of the Product function are usually very large. Large numbers are often shown in Scientific number format (3.43565E12). You can format the numbers as Number format, instead of Scientific format. Remember that the internal precision of Excel is only 15 significant digits and numbers calculated above 15 digits will show the last numbers as 0.
Hope this helps.