Grids for softboxes or beauty dishes or spots prevent the spread of light. The finer the grid the straighter the light, but you also lose light. If you take a spot and aim it at a wall the finer the grid the smaller the spot until in an ideal world it would equal the size of the light source at 0 degrees spread.
The are used to aim light at a specific spot (especially with barn doors for hair eyes, points of interest), change the size of the background flare on a wall. prevent light spill from hitting unwanted things like background in a small studio, etc.
I use them in conjunction with softboxes to get a blend of soft and hard light. The softboxes illuminate the subject, the spots with grids hit the hair and eyes to add saturation and contrast (shadow and sharpness). One of my favorite glam setups is to have a SB above and below the camera. A grid stripbox hitting the back diagnal of the subject and a grid spot with barndoors hitting the front eyes and hair in the other front diagnal. I also made bookends (2 4'x8' white foamcore taped together) to put on either side for additional fill.
I don't think I've posted any with this setup in a long time, but I just did this setup again this past weekend for a 4 model shoot and may post some if I get time.