For glass containers, the goal of surface dealkalization is to render the inside surface of the container more resistant to interactions with liquid products later put inside it.  Since the treatment is directed primarily at changing the properties of the inside surface in contact with the product, it is also referred to as "internal treatment". 
The most common example of its use with containers is on bottles intended to hold alcoholic spirits.  The reason for this is that some alcoholic spirits such as vodka and gin have an approximately neutral pH and a high alcohol content, but are not buffered in any way against changes in pH.  If alkali is leached from the glass into the product, the pH will begin to rise (i.e. become more alkaline), can eventually reach a pH high enough that the solution begins to attack the glass itself quite effectively.  By this mechanism, initially neutral alcohol products can achieve a pH where the glass container itself begins to slowly dissolve, leaving thin, siliceous glass flakes or particles in the fluid.  Dealkalization treatment hinders this process by removing alkali from the inside surface.  Not only does this mean less extractable alkali in the glass surface directly contacting the product, but it also creates a barrier for the diffusion of alkali from the underlying bulk glass into the product.  
The same logic applies in pharmaceutical glass items such as vials that are intended to hold medicinal products.  While many of these items are composed of more durable borosilicate glass, they are also at times dealkalized in order to minimize the possibility of alkali leaching from the glass into the product.  This action helps to avoid undesired changes in pH or ionic strength of the solution, which not only inhibits eventual attack of the glass as previously described, but can also be important in maintaining the efficacy or stability of sensitive product formulations.