When you first arrive in Italy, and your Italian is to say the least poor... You are always very happy to see that Italians easily use gestures when speaking, and if you know how to translate these gestures, it will help you a great deal to get around without actually speaking.
But first things first, you should know that, although very common, gesturing when speaking is definitely not regarded as very classy, especially as gestures often indicate a state of discontentment and irritation! So if you do get into the habit of using your hands, do not exaggerate and do so modestly with limited movements and in any case not in a formal environment.
That said, it is quite fun to learn the different meanings. Some gestures can be used with children and are very accepted, others should be left to an adult-only public being quite rude. You even have cellphone Apps to download emojis of the gestures!
Here is a short youtube video illustrating some of the most common gestures: https://www.youtube.com/watch?v=WwZ6NTV1nRc
And an illustration by Alfredo Casano:
Hope you found this helpful!