Caster sugar is the British term for one of several types of sugars used in cooking and baking. In the U.S., it's more commonly referred to as superfine sugar, baker's sugar or bar sugar. Caster sugar (sometimes spelled as "castor sugar" falls between granulated ("regular") sugar and powdered (confectioner's) sugar when it comes to fineness. It also has the smallest crystal sizes of all white granulated sugars, which allows it to dissolve quickly, even in cold liquids.
Due to all of these qualities, caster sugar is generally used in delicate or smooth dishes such as sponge cakes, meringues, souffles and puddings. It's also used as a sweetener in cocktails, with many bartenders preferring it to simple syrup.
In the U.S., it can be difficult to find caster sugar, as it's not used here as frequently as in other countries. If you're not a picky baker, you can typically swap regular granulated sugar for caster sugar. The end result will probably be a heavier, grainier cookie or cake, although the taste should be fine. You may be able to improve upon your results, though, by employing a few hacks, courtesy of Bob's Red Mill.
One is to use colder, firmer butter when creaming with the granulated sugar. The firmer butter will take longer to mix, allowing the sugar grains time to break down into finer particles. If you're making a meringue, try mixing the egg whites on a low speed. This is also a way to give the sugar grains more time to break into smaller pieces.
Another option is to make your own caster sugar. It's quite easy. All you need to do is put some granulated sugar into your blender, food processor or coffee grinder, then grind for one to two minutes. You'll need to add a little more granulated sugar than the recipe calls for to account for any sugar that gets ground to dust and/or remains in the blender. A good rule of thumb is that 1 cup of caster sugar translates into 1 cup plus 2 teaspoons of granulated sugar.
But do be mindful of how long you're grinding the granulated sugar. If you process it too long, it will turn into powdered sugar. And swapping powdered sugar for caster sugar can give your baked goods a texture that's too thin. It may even ruin the results.