Grid snapping refers to the act of using the Grid Snap button functionality in the beatmap editor. Enabling it will force every hit object that is interacted with by the creator to move to the nearest position along the intersections of the grid, or, in other words, "snapping". The Grid Snap button can be found on the right-hand side of the editor.
The base level of spacing between each sector of the grid can be adjusted by pressing G, or by navigating to View -> Grid Level. Grid snapping can help with aligning objects to one another and attempt to arrange them in neater patterns.