In Italy, the only rail passes covering the whole country are those offered by Eurail. Depending on where you're from, right now Eurail is split into Eurail (for those from outside the EU) and Interrail. There are plans afoot to merge these into one scheme but for right now they're separate. As part of this scheme you can buy a "one country pass". An Interrail (for EU citizens) One Country pass for Italy is 153 EUR for 4 days' worth of unlimited train travel within a one month period. The Eurail equivalent for non-EU citizens is the same price for the same period.
Both passes ultimately have the same terms. You must comply with the host country's rules on mandatory reservations, and pay for those reservations where the host country requires it. For the case of Italy, all domestic high speed trains, of type Frecciargento (FA), Frecciabianca (FB), and Frecciarossa (FR), require reservations — the cost is 10 EUR per reservation. I have found conflicting information on InterCity (IC) domestic trains; some sites seem to say that reservations are not compulsory and others say they are; but on balance it seems that they do at the very least highly recommend reservations during the spring and summer, which cost 3 EUR. You should be able to find the information on the type of train in journey planners etc. This applies to domestic Italian trains — if you're travelling on an international train that happens to travel through Italy you should check whether or not reservations are compulsory.
Interrail and Eurail do NOT appear to be valid on the privately-operated Italo trains.
Thanks to these reservation fees you should consider whether a pass will actually save you money in the first place. I would suggest reading the information on The Man In Seat 61 on this subject.
: Source: European Rail Timetable, Summer 2019 edition
: Source: https://www.interrail.eu/en/plan-your-trip/trains-europe/trains-country/trains-italy