What is the mechanism of halogen displacement? We teach (ad infinitum....) that a more reactive halogen will displace a lesser halogen from a compound.  And yes, the halogen is a halide ion in the compound.  Now I think about it, it's usually in solutions, so the halide is nominally solvated and surrounded by water (as hydronium ions?). 

But how?  

Does the halide lose the electron to give a radical, or does the halogen dissociate to radicals, or to ions, or is there an intermediate Cl2- ion, for example?  I realise this is several questions, but the major question is unaffected by my speculation.  All I have found is the bald statement about displacement and reactivity and the table we always draw.
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.