Special White '00' flour
The names 00 and 0 Flour refer to specifically Italian milled flour that is used for pasta making. You will find that this is also called Doppio Zero just meaning double zero. The grading system is 2, 1, 0 or 00 and indicates to how finely ground the flour is and how much of the bran and germ has been removed. 2 for instance is a wholemeal flour while 00 is the most refined of the three and has the lowest level of bran. It is similar to unbleached all purpose/plain flour, which is a mix of hard and soft wheat, and though while finer, it creates a dough that is silkier and maintains a chewiness when the pasta is cooked.
If you are looking for pasta, bread flour or baking flour, 00 will work for all and you can substitute 00 flour if you run out mid way through pasta making with just plain old high-grade flour. Again this has been refined more so than standard flour making it higher in protein. Pizza dough is perfect with single 0 flour but again it is interchangeable.
Grading systems for flour are used elsewhere in the world as well so the Italian system is not unique. The French have a grading system that is similar but it seems most recipes will call for the Italian 0’s.
To make life more confusing the terms hard and soft get used to also explain flours so to try and put it simply:
Low Protein + Low Starch + Low Gluten = soft flour – 00 flour or high grade flour – use this for pasta, pizza and cakes as you would any high grade flour
High Protein +High Starch + High Gluten = hard flour – semolina flour or standard flour – perfect for bread doughs and most other uses.