Why do bicycle wheels use spokes?

Because if you didn't have spokes you'd have to have solid disc wheels which'd be heavier and quite unpleasant to ride in windy conditions.
To hold the hub for your gears. Also keep your wheel true.

Just fine, thanks for asking. Seriously, there seems to be something missing from the question. Spokes in a bicycle wheel work by all spokes pulling the rim towards the hub. The stiffness of the rim prevents it from collapsing, and if all spokes are equally long and pull equally hard the result is a round wheel.