Post-carbon filters are the last step in water cleaning. This is the same as the last player of defense on a soccer team, right in front of the goal. All of the other filters preceding the post-carbon take care of any dirt or chemicals in water; the post-carbon filter is used to make sure the water tastes excellent and is safe. It's more like a cleanup crew for the end of a party, making sure everything is in tip-top shape before everyone goes home.
Such filters are important not only at home, where they purify tap water to taste better and become safer but also in large factories. In the latter case, it is used by industries that manufacture all sorts of things, which have to be clean and most often with controlled purity: food or paint. For instance, in post-carbon filters, water is assured to be clean; hence, the final product is not tampered with. Whether at home or in a manufacturing facility, post-carbon filters aid in keeping the water clean and potable.