After Matt Damon's character in The Departed graduates the state police academy, he is picked up by Costello ("no more pencils, no more books"), and given a box as a graduation present. Though what is contained in the box is never identified, what are some probable theories as to the box's contents?
The box is a pure Macguffin.
I've heard some theorize it contained the mobile phone he would go on to use, but I doubt this.
Another theory is that it contains money, or at least something valuable to help him get started up - hence why Costello tells him he's earned it.
Having said that, my own theory is that it is just something personal to Sullivan. It doesn't really matter what it is, just that it is something personal which evokes emotion from Sullivan and effectively further establishes the father-son dynamic between Sullivan and Costello for the viewer.
You might be interested to read the script for more information. It goes out of its way to point out that the box could contain anything: