Weighted Keyboards are keyboards whose keys are made to feel like the keys of acoustic keyboards. Since piano keys are made of wood and considerably heavier and provide more resistance than plastic electronic keyboard keys, some keyboardists who are used to piano keys, feel uncomfortable playing electronic keyboards because their keys are light and bounce back quickly after being pressed. Weighted keyboards provide the touch and feel of piano keys on electric keyboards, so that people who are trained on acoustic keyboards can transition more comfortably into the use of electronic keyboards. The feel of weighted keyboards would usually be described/advertised by manufacturers as "hammer action" while non-weighted keyboards use "synthesizer action" so when you buy one you choose which "touch and feel" you are more comfortable with.
for the advantages of using weighted keys over non-weighted ones.