I was reading through technical papers and newsletter about DyMESH and I am curious as to what is the definition of a "watertight" mesh model?

A watertight mesh is one in which each neighboring polygon shares its vertices.  The Tech Session of the Fall 2004 newsletter illustrates and discusses why watertight meshes are important for ensuring that the collision modeling between vehicle meshes is handled correctly.  A collision simulation that results in spikes in the damage region is a sign that the mesh on the other vehicle is not watertight.