Shake to allow finer particles of finished compost to fall through. Larger twigs, rocks, clumps, and trash will remain on top of the screen. If the remains are mainly organic, throw them into another compost pile. If not, it can be disposed of appropriately. One composter I know gets a lot of rocks when he sifts, so he uses the remains to fill holes in his drive.
Sifted compost is easier to handle and spread.
Whether or not ease of application compensates for effort required is a decision you must make on your own behalf. For most composters, the answer is no. I know one guy who lets local yard workers dump grass clippings and leaves at his place. He has to sift before composting to take out coke and beer cans that were raked up with the leaves. Sifting compost removes clumps of matter that have not completely decomposed.