What does a Breakthrough gun do?
The Breakthrough Gun rules are not covered in the Flames of War 2nd Editon or earlier rule books. This is supported by the comments in the FoW 3rd Edition Q&amp;A:

When will you be updating Arsenals to reflect the new rules like Breakthrough Gun and mortars being able to shoot as well as bombard?
A new publication, Know Your Enemy, will be released soon. It includes a complete Late-war arsenal to update all Late-war books. We will be updating Mid-war and Early-war books to match over time. Meanwhile, you can use the Late-war updates to guide you on which weapons are rated as Breakthrough guns and the direct-fire capabilities of mortars.

There is a small blurb on the Battlefront Minature's Flames of War website.

Breakthrough Gun
Some weapons are just so powerful that there is no chance of surviving a hit from them. These heavy guns are often mounted in tanks and self-propelled guns designed to break through enemy defensive lines.
Infantry teams, Gun teams, and Unarmoured vehicles automatically fail their Saves when hit by a Breakthrough Gun or a Bunker Buster. This does not apply to Artillery Bombardments.

An example of a unit with the ability is listed just above this on the same page:

The 12.8cm K81 Gun in Flames Of War

    Weapon              Mobility Range     ROF Anti-tank Firepower Notes
    12.8cm K81 gun      Immobile 48&quot;/120cm   1        17        2+ Breakthrough gun.
    Firing bombardments          104&quot;/260cm  -         4        3+

The Hammer and Sickle supplement also mentions the Breakthrough Gun rule. It also fails to mention any additional information about the rule, which leads me to believe that there isn't much more to the rule (although it isn't definitive proof without access to a 3rd Edition rule book, or the Know Your Enemy publication.

The Heavy Breakthrough Gun rule also returns and applies to the IS-2 and ISU-122. Infantry, Gun tams and Unarmoured vehicles are vulnerable to these massive rounds and automatically fail their save if hit by one.