It seems both "sign" and "initial" mean the same thing, but why does he use those verb in a row?
That's a great question. "Sign" and "initial" actually mean different things. To "sign" something means to put your signature on a document. It acts as proof of identity and intent. Your "initial" is the first letter at the beginning of each of your names. For example, if your name is Jane Brown your initials are, J.B. It is quite common for legal documents to require both your initials and your signature, sometimes you have to sign and initial on multiple pages.