Well, it’s called a punt and there are many theories as to its purpose in a wine bottle.
The most common misconception is that if a bottle of wine has a deep punt it means the wine is better quality. This is not the case but may have been born of some truth. (By way of proving the point Cristal Champagne has no punt.) One theory why this idea came about is from when the bottles were made by hand. They tended to be fairly rounded and so didn't have a flat surface to rest on, by putting a punt in the bottom gave the bottle a base to sit on. This made the bottles much more stable and skilled glass makers worked out that the stronger his glass, the deeper his punt could be, and therefore the more he could charge for his craftmanship. It follows that a winemaker would not then put cheap wine in an expensive bottle.
So, why is it there? As touched on above it is thought to make the bottle more stable. If you have a flat bottom there is more danger of an imperfection causing the bottle to become off-balance, a punt limits this. It has also been suggested that it is simply the mark left by the pontil which holds the glass in place as it is being formed.
These days as the process is mechanised there is an element of the punt, and general shape, size and weight of the bottle, being partly for marketing purposes but also for storage and shipping. It is easier to stack bottles as the neck of one can go into the punt of another. If bottles are ‘connected’ in this way there is less chance of them rolling around and becoming damaged. There is also a theory that the punt reduces the amount of resonance through the glass and so prevents the glass shattering in transit.
The punt also helps with the service of wine as one can put ones thumb in the punt and tilt the bottle more elegantly. There is a Danish story that tells how the wine server would often be more familiar with the gossip within the town than his master. The servant would indicate to his master whether his guests were trustworthy by using a thumb in the punt or not.