It’s a local celebration dedicated to the city patron - San Ranieri, of course. It takes place in Pisa on June 16 of every year.
It consists of a very particular thing: the leaning tower, the Dome, the Baptistry, and all the houses along the River Arno are illuminated by little lights and sometimes candles to create a real romantic and medieval atmosphere during the night. At midnight, or sometimes after, there is a big firework show on the River Arno that you can’t miss.
Some advice for you: the day of San Ranieri is a holiday, so you won’t find many shops, offices, or museums open, so be sure to check if the things you planned to visit are open to the public on that day. The second thing is that on those days, Pisa is really overcrowded, so you’d better book your hotel and restaurants if you want to have the chance of eating something. There are many takeaway stands in the narrow streets around the city center, though. The third thing is don’t expect to find a car park, a bar, a pizzeria, or a restaurant with a place free. You really have to fear the crowds. Two years ago, I went to this celebration, and it took 2 hours for us to leave Pisa with the car because of the traffic jams. It took two hours to reach the freeway, which was a half mile far from the car park.