"Bottom fermentation" is one of the two main types of fermentation which take place during beer production; the other being "top fermentation". A third less common type would be spontaneous fermentation (a natural beer fermentation process taking place in the wild). Typically, only one fermentation process occurs during production (either bottom, top, or spontaneous fermentation). It basically describes what happens to the yeast during fermentation- some yeast float to the top of the liquid during fermentation, while some types of yeast sink to the bottom. Which type of fermentation takes place, depends on the type of yeast used in the process. So to answer your question, if it effects the type of drink (and taste), the answer is yes. It's not so much whether the yeast sink to the bottom or float to the top that affects the taste/style, but it is rather due to the type of yeast which determines what will happen to during fermentation (float to top/sink to bottom). For instance, lager strains of yeast typically float to the bottom.
"Some of the lager styles made from bottom-fermenting yeasts are Pilsners, Dortmunders, Märzen, Bocks, and American malt liquors."
"Top-fermenting yeasts are used for brewing ales, porters, stouts, Altbier, Kölsch, and wheat beers."
A more in-depth summary can be seen at the Beer Advocate's Yeast Guide.