Only one time in the movie do we see Four's entire tattoo.
We see it in the scene directly following the one where Four takes Tris into his own Fearscape and Tris sees Four's deepest fear, being beaten with a leather belt and buckle by his father Marcus starting in childhood.
Usually Four stands and calms his breathing and heart rate. (This is standard technique for "flooding" developed by Edna Foa.) Tris however grabs Marcus's belt, punches Marcus and Four protects her from Marcus, thus initiating a new response in Four.
In these two images we have the complete history of Four/Tobias's childhood, in reverse sequence for the viewer.
The tattoo is a record of his beatings. On a child's skin, a leather belt is going to leave terrible welts, cuts and permanent scars. Not like Patsy's beatings in 12 Years a Slave nor like this slave:
|A horrifying explicit vision of Nietzsche's Torturous Inscription of the Body|
But you get the idea. To a child it is a terrible thing to endure beatings that leave permanent markings.
Down the center of Four's back on his spinal cord are the five faction symbols.
So with this piece of dialogue we know that every time Tobias displayed curiosity - forbidden in Abnegation - which is linked to intelligence, or bravery, honesty, happiness or kindness Marcus forbid it. And he not only forbid it - the way Beatrice was forbidden - but he was also punished unmercifully for being a curious, kind, intelligent, honest, brave and happy child until he learned never to show any of those feelings. Ever.
The tattoo clearly shows the lash marks probably covering some scars. It clearly shows all five of the factions, desires, attributes, a well rounded person who was emotionally mature might have.
But exposing the tattoo reveals both shame and desire.
In revealing what he has concealed to Tris in his Fearscape and on his back he is confessing shame and opening himself to vulnerability. (Badiou:In Praise of Love)