Avignon’s greatest claim to fame is as that it was the capital of the Christian church for almost 100 years. In 1309 Pope Clement moved the Papacy to Avignon. Six popes later, Gregory 11th, moved back to Rome, beginning the “Great Schism” during which two popes reigned, one in Rome and one in Avignon. As it was, the city remained the property of the Vatican until the French Revolution.
The old town is completely surrounded by a wall with towers at the many gates and battlements along its top. The city was important to the Roman empire, helping guard the roads to Gaul. When it housed the Papacy, the walls were raised to their current height curtsey of the popes.
You can circumambulate the city easily in two hours or less. The eastern part of old town is where the majority of the tourist attractions are, including a walking only section with lots of shops. The rest of town is mostly local residences.
The Saint Benezet Bridge, mentioned above is Avignon’s second greatest claim to fame.