Origin 100 BCE to 200 CE
Emptiness means empty of inherent existence, of any self-standing nature that a thing possesses independently of causes, conditions and conceptual designation. It does not mean that nothing exists. Nagarjuna, whose work founds the Madhyamaka school, spends much of his time rebutting exactly that reading, and warns that anyone who takes emptiness itself as a position to be held has misunderstood it as badly as the error it was meant to correct. Emptiness is a medicine, and it is not to be swallowed as a thesis.
The connection to dependent origination is the heart of it. Things arise dependently; what arises dependently does not have an independent nature; therefore dependent origination and emptiness are the same insight stated twice. This is why emptiness does not entail nihilism: it is precisely because things are empty that they can function, arise and change at all.
The doctrine is worked with two levels of truth, the conventional, in which ordinary statements about tables and persons are perfectly true, and the ultimate, in which no such thing is found to have inherent existence. Confusing the levels produces most of the misreadings.
There is a genuine and unresolved disagreement downstream of this. Alongside Madhyamaka, the Mahayana developed a literature on buddha-nature which speaks in strongly positive terms about something luminous and present in all beings, and it is not obvious how to reconcile that with a doctrine of emptiness. Tibetan scholasticism divided over it: one position holds that everything, including buddha-nature, is empty of its own inherent existence; the other holds that ultimate reality is empty only of what is extrinsic to it and is not empty of its own qualities. The debate has run for centuries, is doctrinally serious, and is still live between institutions.