In general, a sieve separates by physical means wanted/desired elements from unwanted material using something such as a mesh, net or other filtration methods; but it is also used for classification of powders by particle size, or for size measurement as an analytical technique. The word "sift" derives from this term. A strainer is a type of sieve typically associated with separating liquids from solids. A colander is a similar device.
Another use of a sieve is to incorporate air into flour and it also has the added benefit of removing and clumps and lumps. In old recipes, it was always advised to sieve flour into the mixing bowl before use, but this was usually for the main purpose of removing bugs, mouse droppings, flour weevils and other foreign bodies.
Finally, sieving icing or caster sugar over a dessert or other sweet products (pies, pastries, doughnuts, etc) can produce a very professional and pleasing-to-the-eye effect. A medium-sized vegetable sieve (clean and totally dry and free of moisture or fat/grease), or for smaller quantities a tea-straining sieve (5-7cm in diameter), is ideal for this. If you find yourself doing this often, there are dedicated sugar shakers available. Cocoa powder (as well as cinnamon powder) can all be used for similar decorative and flavouring purposes.
Tip: Put one or two items - (but not too many!!!) such as cutlery (fork, knife, spoon), an upside down round ramekin or other similar shaped objects (stars, crescents, etc) on a large, preferably coloured flat serving plate, then sprinkle evenly all over with sifted sugar/cocoa/cinnamon or cobination thereof. Carefully lift the items off without touching the plate with your fingers (tip of a sharp knife is useful for this) and hey presto! - silhouette images which you can place your food on or around. Just like Ainsley does it on RSC!