What is the mechanism of halogen displacement?
I'm guessing your talking about the halogen displacement reactions:

$$\ce{2NaBr + Cl2 -&gt; Br2 + 2NaCl}$$

which is a redox reaction: 


$\ce{2 Br- -&gt; Br2 + 2 e-}$, bromine loses electrons (is oxidised)
$\ce{Cl2 + 2e- -&gt; 2 Cl-}$, chlorine gains electrons (is reduced).


For more detail look in to the redox potentials, this explains what will reduce what.