This square is one of the most important ones in Genova and is in the heart of the city. Many Genovese meet here both in the morning and afternoon to speak, read, or go have a drink or snack. It has a beautiful fountain in the center and from the square you will also see the Via XX Settembre, where there are shops of all the important brands.
What comes out in the picture is the Piazza della Vittoria, at the end of XX Settembre. Piazza Corvetto is another square, at the end of Via Roma, but in the downtown area of the city. I suggest visiting both of them, but especially the vantage point of the photo (which is the Piazza della Vittoria.)