Animating articulated chains — move shoulder, arm and hand follow mechanically. Intuitive control but tedious when target position must hit exact point. IK faster for that.
When motion capturing a character or rigging a digital character, you work with linked joints — shoulder, elbow, wrist depend on each other. Forward Kinematics means: you move the topmost joint (the parent), and all downstream joints (the children) automatically follow. Rotate the upper arm by 45 degrees, and the whole arm rotates with it — no intermediate calculations, no inversions. The system propagates the movement from top to bottom through the chain.
The practical advantage lies in intuitiveness. On set or in the anim viewport: you grab the arm at the shoulder, and it feels natural because it works in reality. Direct, understandable control — exactly what your brain expects. The computational power required is also low; the system doesn't need to optimize iteratively. For carried movements, striking techniques, or even camera rigging with multiple cranes or arms, this is often the faster solution.
The catch: if you want to bring the hand to a specific point in space — for example, onto a table or into another character's face — you have to manually adjust the upper arm, forearm, and wrist to hit the target. This is iterative, prone to errors, and with multiple joints, quickly becomes frustrating. That's why Inverse Kinematics (IK) is used for such tasks: you place the hand, and the system calculates backward how the upper and lower arm must be positioned. FK remains relevant nonetheless — for organic, natural movements where control is top-down (animal locomotion, spine movements, tentacle animation).
In practice, you often combine both: FK for the rough pose, then IK for hand positioning. Or a hybrid rig with FK defaults and optional IK handles. For extreme deformations — rigging tentacles, tails, hair bundles — FK is sometimes the only practical method, because IK can get stuck in local minima with many joints. Important: don't mechanically weigh it against Inverse Kinematics. FK is not obsolete, but a fundamental tool for motion characters.