Baking has much in common with the general laws of physics, chemistry, and precision. It's difficult to wing things on the go when you're baking, where something as little as sifting ingredients can be the difference between a light and fluffy cake versus a dense and heavy one.
Sally's Baking Addiction, for example, explains that there's a significant difference between a recipe that mentions sifted after a dry ingredient, like flour, and one that mentions sifted before the ingredient. The former means that you should scoop out a cup of flour and then sift it, whereas the latter means that you should be measuring a cup of flour that has already been sifted. Getting something as seemingly inconsequential as the order of sifting wrong can skew the proportion of ingredients and have a significant impact on the result. Rotary Vibrating Screen
Sometimes a recipe may not mention sifting at all. In most cases, it's better to sift ingredients anyway. Unless you're a regular baker, All Recipes says that you probably need to sift dry ingredients like flour, powdered sugar, and more importantly, cocoa powder, which are all prone to clumping.
According to All Recipes, not only is sifting cocoa powder a good idea to get rid of any clumps, but it's especially important when you're making light batters for intricate bakes. In that case, it's important to get as much air as you can through powdery ingredients, like cocoa powder, which will fluff up when you sift them.
King Arthur Baking also points out that sifting is even more important when it comes to cocoa powder that is unsweetened. Unsweetened cocoa powder contains cocoa butter, which can form lumps in the dry powder and prevent it more mixing well in batters. Unless you want pockets of bitter, dry cocoa powder in gooey brownies and moist chocolate cakes, it's a good idea to sift it first.
Test Sieves In case you don't have a sieve or a sifter, regular tea stainers can sift cocoa powder just as well (via Art Chocolat). Alternatively, if you can't be bothered to add the extra step altogether, it's also possible to break up the lumps with a whisk when you add the cocoa powder to a mixing bowl with other dry ingredients. While this will get rid of any large clumps, it may not aerate the cocoa powder and sift it as finely as a sieve would.