Magic variables are any variable that has, well, magic attached to it. Magic is an internal perl facility that lets perl intercept reads and writes to a variable and call some code to satisfy the read or write request.

Tied variables, for example, have magic. When you read or write to a tied variable perl calls the code in the package the variable has been tied to. Many perl special variables are magic--for example $! is magic. When you read from it, perl goes and fetches the contents of errno, which is an integer that notes the last error a system call threw.

There's not much to know or learn about magic in general unless you want to go dive into the innermost guts of perl, in which case perlguts and perlapi are the place to go. Generally you'll use a specific type of magic, such as tying, rather than just magic in general.