I’m finding this excessively hard to find information on, but I assume it’s not useless, considering modifying it in a texture stage using “matrix” does…something. Help?
Since Unity doesn’t seem to have any 3D texture support, I’m assuming you’re not dealing with 3D textures and 3D texture coordinates (in which case it would just be the 3rd coordinate). In case of 2D UV, the W is the extra dimension that makes the coordinate “homogeneous”: Homogeneous coordinates - Wikipedia
Since uv coordinates are supposed to be points that can be translated by the texture matrix, w should have the value 1. It probably already has this value and not changing it will make your transformations work as expected. If it has any other value, all your translations will be affected or even ignored (when w is set to 0).
All values other than 1, with no other transformation involved, seem to scale the UVs about the origin.
Homogeneous coordinates are basically equal to the values of the normal coordinates divided by the value of the “extra” component (the W in this case).