Q:

Point Clouds associated with Grid Structures?

This page says the following:
point clouds coming from structured/gridded files (such as PTX, DP or FARO) are now associated to a simple grid structure. This structure will mainly be used to export the cloud in a structured format, but it can also be used when computing normals for instance.

What kind of grids can be associated with a point cloud?
Are there format standards and definitions for those kinds of grids?

A:

If you read a little further on that same page, there is a explanation of what kind of structures can be associated with a point cloud.
However I think that the word "gridded" files might be confusing you. 
As you can read here: A gridded file format is just a file that contains not only XYZ, RGB and/or intensity information but also some matrix that can be used to generate planar views of scans.
Here is the specification of the PTX format.

