These strange cathegories are based on the fact that a real Italian Lunch, or Dinner, should be made of different dishes, from the lighest, to the pasta, to the meat or the fish ( along with some side dish) to the dessert.
These are the cathegories you will find when reading an Italian Menu.
PRIMI: (Literally "First") They always include the Pasta, with fish, or meat, or vegetables or cheese. When you say "I'll have a "Primo" you're saying you will eat some Pasta! Rarely you can find Soups too in this cathegory.
SECONDI: (Literally "Seconds") Here you will choose between the most "important" dishes of the lunch, and you will be able to choose between the "SECONDI DI CARNE" (Meat) or "SECONDI DI PESCE" (Fish)
CONTORNI: (Side dishes): usually a salad, or fries or roast potatoes.
DESSERT: Here you will find our best cakes or icecream, Cream or Chocolate, or Fruit or some typical regional dessert.