A net, in its primary meaning, comprises fibers woven in a grid-like structure. It blocks the passage of large items, while letting small items and fluids pass. It requires less material than something sheet-like, and allows seeing through.
The adjectives reticulated and retiary both mean "net-like".
Most of the other meanings of the term are by analogy with the use above.
Safety net is also used figuratively, see e.g. social safety net.