I believe it's just a standard reference point when measuring and drilling the finger holes.
From my experience with a few guys who drilled on the PBA truck, they like to drill the thumb hole 1st and then drill the fingers. They measure out the lines ahead of time and use the 5/16th or some other reference intersecting point for the finger holes.
For instance when I drill my own balls, I like to use 1/2 of the finger size from the bridge line. This would put the span line right in the center of the finger hole.
Some guys do it different. Not sure where the 5/16ths came about, but somebody else maybe able to explain that better.