These walls are in fact old Roman aqueducts - stretching for miles in either direction. The first aqueduct (immediately behind Saint Polycarp) is shorter and newer, having been erected by Pope Sixtus V in the 1500's. The further aqueduct, a little over a hundred meters forward, is in the heart of the Parco degli Acquedotti (Park of the Aqueducts) and is much older - from 312 B.C. Though crumbling and derelict, these arched stones look ever taller as you approach them. Though not a wonder to the eyes like one of Rome's Basilica's, these aqueducts and their quiet grandeur are a wonderful location to visit for quiet reflection or reading or even to have picnic lunch. Cheaply getting away from the hassle of the City of Rome is an end successfully accomplished in a visit to Parco degli Acquedotti.
Sources: Guide to the aqueducts of ancient Rome. Aicher - Bolchazy-Carducci Publishers - 1995 Eyewitness Travel Family Guide Rome. DK TRAVEL - 2017