Just as we saw Tris get tattooed as a rite of passage, Four does the same thing in "The Initiate." He describes his thought process:
That is what this tattoo will be, for me: a scar. And it seems fitting that it should document the worst memory of pain that I have. (2.115)
The scars he's talking about are the scars his abusive father left on his back with a belt. Um, yeah. That's highly unpleasant.
For Four, the tattoo both covers up the scars and reminds him of them. They show who he used to be, and they show who he can become. When he later has Tori start on a tattoo of all the faction symbols, we see how he wants to be a uniting force, someone who can bring all the factions together instead of keeping them apart.