The Hell-Volhard-Zelinsky reaction involves the halogenation of carboxylic acids at the α carbon. During the reaction, a carboxylic acid’s OH group is replaced by a bromine atom from the PBr₃ catalyst to form an acyl bromide. This compound can then form an enol via tautomerization; this allows for a second bromination to occur at the α carbon by Br₂. The following picture is the reaction scheme of this process.

  

Hydrolysis of this α-bromo acyl bromide forms an α-bromo carboxylic acid, by means of a nucleophilic acyl substitution. To speed up the reaction and to ensure that the acyl bromide intermediate is not regenerated during this step of the reaction due to lack of nucleophilic solvent, a molar equivalent of PBr₃ is used. The following mechanism is a depiction of this part of the reaction.  

An example of a Hell-Volhard-Zelinsky reaction, would be the halogenation of acetic acid at the α carbon with PBr₃. In this step, a bromine from PBr₃ would replace the hydroxy group on the acetic acid to form acetyl bromide which, after tautomerization into an enol, would be introduced to Br_2. This step of the reaction is an attack of the α carbon by Br and would produce bromoacetyl bromide which, when reacted with yet another acetic acid molecule, would form 2-bromo acetic acid and bromoacetone. If the R group was taked off of the products in the preceding picture, they would be 2-bromo acetic acid and bromoacetone.

Sources:

http://en.wikipedia.org/wiki/Hell-Volhard-Zelinsky_halogenation 

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