Forward
A grid is a pattern of black fabric that you mount typically on the front of the softbox instead of the usual white fabric. The grid will effectively stop or dampen all light that tries to travel sideways relative to the direction the flash is pointing, and hence make most of the light travel in the same direction.
Although the softbox itself is coated with a reflective fabric on the inside and and hence designed to send all the light forward, the forward direction is still much wider than the front of the softbox itself. The grid helps limit the sideways travel by only allowing the light moving straight forward to continue, the rest is blocked or dampened.
I use the grid to give more specific direction to the light, if for example it is important that the light bouncing from the floor or the ceiling is minimized. Notice that the grid dampen the effect of the flash all things equal quite significantly, so especially if you shoot the flash in manual mode, you need to factor in the effect of the grid when setting the flash power.