General magic can be used to define many different things. Here we will classify it as the study of magic with a variety of objects using different common techniques. Instead of focusing in a single object, like card or coin magic does, you seek to have a repertoire that works with napkins, matches, rubber bands and etc..
Most magicians end up having a “general magic repertoire” since they might start with cards but pick a rubber band effect they like, some cube magic after a few months and etc..
If you are interesting in learning with a variety of objects from the beginning you have several great options (specially books) that will give you a lot for your money.
The main advantage of learning this sleights is that you become a very versatile performer. Many times you will be able to perform with what you find in a regular kitchen or living room.