Q:

'Read before The Royal Statistical Society ' What does it mean? 

In the header of several journal articles, I have seen this:
Read before The Royal Statistical Society at a meeting organized by the Research Section on Wednesday, May 5th, 2004, Professor J. T. Kent in the Chair
What does it mean for a paper to be read before the Royal Society ? 

A:

This means that the paper was presented to the members of society who were present at the meeting noted.  
I am more familiar with this language in much older papers.  I believe its use here is a holdover from a time when paper would be presented by a Fellow of the society (who may have been the author of the paper, or otherwise) to the assembled members of the society.  For example, neither Darwin nor Wallace were present at the 1848 meeting of the Linnean Society at which their joint papers were presented; instead the papers were read by secretary John Bennett.