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How to Read This Function

Re Mathematica 5.0.

has an example that uses

    ff[a_?(Refine[# > 0] &)x_] := a*ff[x]

Thus, ff[2x] returns 2 ff[x] ("If $Assumptions has no effect on 
ff...then ff pulls out positive numeric factors."

What's the right way to interpret the function's lefthand side?  My take 
is "Split the passed argument (#) into variables a and x, where a is the 
product of all positive numeric factors and x is the product of what 
remains."  If this is correct, then I don't know for sure how the 
lefthand side says this.

Must the argument be a product?  If so, then how is the lefthand side 
saying this? 



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