Battuto literally means 'beaten, whipped', like a beaten egg (uovo battuto). But most commonly it is used as another word for soffritto or a French mirepoix: a mix of finely chopped stuff that is the base for a soup or sauce. Usually it's onion, garlic and parsley, fried in olive oil. Sometimes it may include prosciutto, pancetta or lardo, maybe carrot and celery, olives, capers or other ingredients.
A battuto alla romana is parsley, celery, lardo and onion (and sometimes garlic). With the addition of tomato, a big battuto can become a very simple soup: minestra al battuto.