The Grabber tool is one of the three main edit tools in Pro Tools. When used in the Edit Window the default Time Grabber tool is useful for moving clips around the timeline. It selects entire clips with a single click (you can achieve the same thing by double-clicking on a clip with the selector tool) and once selected clips can be moved horizontally and vertically on the timeline. However there are two alternative versions of the Grabber Tool, what about those?
Separation Grabber Tool
The Separation Grab tool can be used with the Smart Tool and is useful when separating clips from edit selections, particularly across multiple tracks using the P and semicolon shortcuts to move or extend edit selections vertically.
Object Grabber Tool
The Object Grabber Tool allows the selection of non-contiguous selections, with the addition of modifiers it is the quickest way to make complex selections on Pro Tools. See these demonstrated along with a few other selection based tips in this tutorial video.
Smart Tool
The Smart Tool combines the Trim, Grabber, Selector and Fade tools into one and is so useful that most of us spend the majority of our time in it and by default that means we are usually using the Time Grab tool. There however two other Grabber tools available: The Separation Grabber tool and the Object Grabber tool.
There are other contexts in which the Grabber tool comes into play, for example when editing automation playlists or MIDI but these techniques for manipulating clips are real timesavers if you commit them to memory.