How does the fingerprint on the bullet work in Dark Knight?

If you're looking for a real-life application of this scene, I can't say with any certainty if this technology exists or is merely a plot device.

What I can tell you are the mechanics of this scene, however.

Upon arriving at the crime scene, Bruce sees a bullet hole fired into the brick of the apartment. While obtaining this evidence, he says to Gordon that he's going to obtain fingerprints off of the shattered bullet in the wall.

He then returns to the batcave to use a minigun filled with different ammo sizes in order to gauge what kind of bullet he loaded into the chamber, matching the impact of a control brick with the brick he obtained.

Using the information of the size of the bullet, he is able to digitally reconstruct the bullet, and run an analysis on it for fingerprints (The real stretch of this whole scene).

Using the fingerprint information, he is able to compare it to a criminal database of Gotham in order to determine the name of Melvin White (a known Joker alias for comic readers).