What types of damage, in general, does the compulsory third-party liability insurance cover?

The compulsory insurance covers, up to a limited amount, the civil liability of the vehicle's driver when damage — both personal injury and material damage — is caused by traffic incidents.
Insurers will provide us with the accident report form (parte amistoso) that we can use when an incident occurs, to expedite the handling of damages caused in the accident. In it, we will include the personal details of both parties involved and a small diagram of what happened.