There are multiple reasons. The most simple answer is because the rain that we consider acidic has a low pH; it has a higher amount of hydrogen ions.
Why does this happen? One is because of the release of sulfur dioxide into the environment to which we humans often contributed. However, it is also possible that increased levels of nitrogen oxide would have this effect as well. And nitrogen oxide can be released through lightning or volcanic eruptions, so these are occurences in nature that don't have anything to do with humans.
