I think that technically they are known as rails (even though some people think that's what the cushions are called), but I might also use edge, as SwissPete has suggested. Whatever you think the person will understand.
This site is interesting and supports "rails": RAILS. (General) The top surface of the table, not covered by cloth, from which the cushions protrude toward the playing surface. The head and foot rails are the short rails on those ends of the table; the right and left rails are the long rails, dictated by standing at the head end of the table and facing the foot end. http://www.billiardworld.com/glossary.html