Espresso Romano, also known as espresso roma, is a broad term referring to espresso served with lemon. Ideally it's a lemon peel on the side, but in some places it's served with lemon juice already added to the drink (this is bad, see below). In all my searching I haven't been able to figure out it's definite origin, but I've heard a few interesting stories.
According to some, it's a throwback from a time when bars didn't sanitize cups properly. The espresso would be served with a lemon peel to rub on the edge of the mug. Some people like the added taste, so that's why it's still available.
More commonly I hear it's purpose is to counteract the foul taste of bad espresso. Apparently the water in Rome is so bad, lemon is commonly served on the side to kill the flavor. Either that, or it's added to cover up the foul taste of most American made espresso.
The peel should be included on the side, although is sometimes already squeezed into the espresso. This is bad, because the citric acid will cause the crema to break up immediately. If you would like to enjoy the flavor of lemon in your espresso, it is recommended you rub the peel on the edge of your cup so as to minimize the acid's contact with the coffee.