I think the best explanation, how Lisp macros are different from most other macro system is, that a Lisp macro is a function executed during compilation. It gets fed the parameters passed to it in literal form and then computes the source to actually compile by the compiler.

The power of this is that this function is also written in plain Lisp and it also sees all definition already existing in your Lisp image. Also, it is completely unlimited in power. So while being run, or as it is called "during macro expansion" the function could google for one of the things passed and use the result to create the output. Of course, this is not a practical example, but shows how flexible the system is.