In a Stock name such as iron(III) sulfate, the roman numeral tells us?

Some elements, including iron, can have different oxidation states in compounds. The roman numeral indicates the oxidation state, for example:

In Copper (I) Oxide, Cu_2O, Copper has an oxidation state of 1.

In Copper (II) Oxide, CuO, Copper has an oxidation state of 2.

These 2 compounds have different properties.

So, the Numeral tells you what version of Iron Sulphate you are getting.

You can also consider this roman numeral as the valency of the atom, as it has several valencies. Anyway, that's how I came to be know to these, until later, I learned about oxidation states.

Hope it helped!:)