Reason behind conversion of acid to acid bromide in Hell-Volhard-Zelinsky reaction
The $\alpha$ halogenation occurs through the enol form. 

The formation of the acyl halide is key because carboxylic acids do not form enols readily since carboxylic acid proton is removed before the $\alpha$ hydrogen. Acyl halides lack the carboxylic acid hydrogen. 

The phosphorus halides form the acyl halides readily because phosphorus has a huge affinity for oxygen. 
Sometimes, phosphorus tribromide is not enough to form the acyl halide but, since there is also bromine in the media, phosphorus pentabromide is formed which can form acyl halides even of solid acids. 

The halogenation is performed by the $\ce{X2}$, either bromine or chlorine. 
When $\ce{PBr3}$ and $\ce{Cl2}$ is used, the alpha-chloro acid is obtained and not the bromo acid.