A grid usually refers to two or more infinite sets of evenly-spaced parallel lines at particular angles to each other in a plane, or the intersections of such lines.
The two most common types of grid are orthogonal grids, with two sets of lines perpendicular to each other (such as the square grid), and isometric grids, with three sets of lines at 60-degree angles to each other (such as the triangular grid). It should be noted that in most grids with three or more sets of lines, every intersection includes one element of each set.
There are other types of planar grids, like hexagonal grids, which are formed by tessellating regular hexagons in the plane. These are often found in strategy and role-playing games because of the lack of single points of contact characteristic of isometric and orthogonal grids. The collection of cells created by a grid is often called a "board" when these cells are used as resting places for pieces in a game.
Grids can be generalized into 
-dimensional
space by using the centers of packed 
-spheres or 
-cubes
as the points.
