There are several types of sugar used in baking, one of the most important is icing sugar, which is also known as confectioners sugar or powdered sugar. It is used in many elements of baking, mainly for items like icing or butter creams. It is a fine sugar, much finer than a caster sugar, and therefore is often used in recipes that call for the sugar to be incorporated into a fat (as is the case with buttercream).
It is possible to produce icing sugar at home if you don’t have any, but you will need access to caster sugar and a blender or food processor. Icing sugar when bought from a shop is basically a finer milled version of caster sugar, that is often combined with an anti-caking agent like corn starch.
When making it at home, the best way to begin is to take a food processor, make sure it is totally dry, and blitz the caster sugar to a fine powder. You can do this with something like a pestle and mortar, or even a coffee grinder. If need be and you have it available, you can add a small amount of cornstarch to help to stabilise the sugar and prevent it from forming into a cake.
When blending the sugar, it is important to consider the amount you are trying to blend at one time. If you put too much into the food processor then you won’t get a fine or even grind.
You can also produce icing sugar using granulated sugar, but there is an important consideration when doing this. It is likely when using granulated sugar you won’t get as fine a grind, so if using for something like buttercream it is likely to be a slightly more grainy finish. As a result it may be worth considering whether or not to try and find caster sugar to turn to icing sugar for products like this, unless of course you can buy actual icing sugar itself.