Used to drag a group of vertices around. Grab selects a group of vertices on mouse-down, and pulls them to follow the mouse. And unlike other brushes, Grab does not move different vertices as the brush is dragged across the model. The effect is like moving a group of vertices in Edit Mode with Proportional Editing enabled, except that Grab can make use of other Sculpt Mode options (like textures and symmetry).
Enabling Grab Active Vertex also enables a dynamic mesh preview which generates a preview of vertices connected to the active vertex. This helps to visualize the real geometry that is being manipulating while sculpting with active modifiers.