I'm a little bit confused by the terminology here. What exactly is a "transaction", in a lower-level sense? What does it consist of? Is it pure CPU processing of one data structure to another? Is it shuffling things around in a (local? remote?) database? Is negotiating a transaction with another mainframe somewhere else over TCP?

It matters, because otherwise any kind of performance number is meaningless. If it's just CPU processing, then 1.1 million is not that much. If it's doing some sort of network handshake/transaction with other mainframes, then it's VERY impressive.