Brewing beer during the 1800's was a local endeavor. Individual villages and towns could have as many as twenty local breweries. By 1850, large cities like Munich, Prague and New York had hundreds of breweries operating. The main limiting factor for brewery growth was the short shelf life of the beer, allowing only a distribution time of 3 to 10 days before the beer showed a sharp drop in quality. This poor quality was primarily due to yeast autolysis and beer spoiling organism, and protein/polyphenol formations.
What was the impact of filtration? Brewers became able to produce a beer that was (more or less) free from spoilage bacteria and even more important, free from yeast. Beer quality became more reliable and constant as the consumer enjoyed a range of beer brewed in various regions. A global market was created. At the first world exhibition in Paris in 1889 you could already taste filtered beers from all over the world.
Beyond removal of yeast and bacteria from beer, breweries today use filters (and aids) to remove proteins, polyphenols, short and long chain carbohydrates and other substances that cause beer haze. Other filtration processes that contribute to brewery quality and productivity are beer recovery, water (brewing and service), CO2 and air/steam.