As of 1992, the Italian government passed a law allowing people of Italian descent to apply for and obtain Italian citizenship. Italy requires you to prove your Italian ancestry with proper documentation and does not require you to renounce your current citizenship, which allows you to hold multiple passports and be a dual citizen.
Once a person is granted Italian citizenship, they are allowed all of the rights and privileges of those born in Italy and can obtain a passport to live and work anywhere in the European Union.
These are just the basic rules. Some factors are not mentioned here and can affect eligibility for Italian citizenship.