Mechanical keyboards use mechanical switches made from springs and plastic slides on the keys' handles to register keystrokes and give tactile and auditory feedback. Non-mechanical keyboards use a single plastic foil or muddy rubber dome to provide feedback, or two separate layers of foil that are assembled to detect keystrokes.
If you are a heavy user who is using a keyboard at a fixed place like a desk, writing text or punching code for hours, or if you are an extremely fast typist, a mechanical keyboard is the right choice.