There are hundreds of thousands of variable stars observable from Earth. To properly study a star, one needs to follow it over a period of time. Astronomers simply don't have the resources to monitor them all. This is where you come in.
Observing a variable star is relatively simple. You basically compare the brightness of the variable star with that of nearby non-variable stars and then report that brightness to the AAVSO. This can be done with or without a telescope or binoculars. The easiest way to get started is by making observations with your eyes. However, more sophisticated measurements can be made with digital equipment such as DSLR or CCD cameras.
Professionals need amateurs to not only help monitor variable stars, but also to help study them. There are simply too many stars and too few professionals to fully explore the field of variable star science. As a result, over the past century our members have been involved in discovering new variable stars, categorizing discoveries, testing (and proposing) theories of variable star science, etc. The AAVSO has published a peer-reviewed journal since 1971 that consists mainly of papers written by our members. The journal is indexed in professional astronomy catalogs and carried by university libraries across the world.
Approximately half of our members do not actively go out and observe variable stars. Instead, they contribute by applying their computers and skills in other areas (a.k.a. armchair astronomy). This is a form of citizen science we call citizen astronomy, because it is the only area of science where amateurs can contribute at such a high level. Observation is just one phase in the scientific process. There are lots of other ways to contribute scientifically.