Why is it important to support your wrist while using the keyboard?

Prevent CTS/OA. Repetitive movements may cause osteoarthritis changes. Using fingers often, moving the ligaments and tendons of the hand may cause carpal tunnel syndrome which is irritation or compression of the median nerve at the level of the wrist debilitating the hand and very specific areas of the hand and fingers.
More extension. Actually, the wrist support itself is not as important as holding the wrists in an extended posture during typing. Ideally, the chair would not have arm rests, the elbows below the keyboard and the wrist slightly extended during typing with fingers lightly touching the keys. Often mouse pad supports actually flex the wrist making matters worse. Typing in splints should be avoided.