The Italian Game starts 1.e4 e5 2.Nf3 Nc6 3.Bc4. White develops the king's knight with an attack on e5, then puts the bishop on its most active diagonal, aiming at f7. At the start of the game f7 is the weakest point in Black's camp, because only the king defends it.
Black has two main answers. 3...Bc5 is the Giuoco Piano, Italian for 'quiet game', and leads to a slow fight in the centre. 3...Nf6 is the Two Knights Defense, which counter-attacks e4. Against it White can play the sharp 4.Ng5, which leads to the Fried Liver Attack, or keep things calm with 4.d3.
The Italian is popular at club level because the plans are easy to understand. It is also one of the main weapons of elite players, who prefer the slow 4.c3 and 5.d3 setup shown below. That line keeps plenty of pieces on the board and gives the better player time to outplay the opponent.