The climate in Italy varies quite considerably from north to south, and also how far you are from the sea or the mountains. Generally in the north, winters can be very cold with snow, particularly up in the Alps and the Dolomites where there is good skiing. Further south the winters are mild, or even warm, but with a chance of rain. In the summer temperatures in the north are hot and the major cities can become humid. In the south summer temperatures are particularly hot and dry.
If you’re going on a sightseeing trip, the best time to visit Italy is in the spring (April to May) or the autumn (late September to October) when the weather is still sunny but a bit cooler, particularly if you plan to walk around cities or visit archaeological sites where there is little shelter from the sun.
On the other hand, if sun and relaxation are your top priority, then June through to September are the best months for hot sunshine, particularly on the coast where there are sea breezes, or up in the Alps or Apennines where temperatures are less intense.