Emptiness (Sunyata) refers to the lack (or sometimes the perception of this in some uses) of an atman or permanent essential identity in phenomena. There are two aspects to emptiness:
the lack of essential identity in external phenomena
the lack of essential identity of oneself
Emptiness certainly isn't about nothingness, it refers specifically to there being no findable ultimate nature to things. It is because things lack an essential nature that they are in a continuous state of transformation: birth, growth, ageing, sickness and death are all emptiness. If they had an essential identity, change would be impossible.
Another way of talking about emptiness is to say that all phenomena arise conditionally or dependently on other phenomena.
It is also very closely related to (or the same as) impermanence. It is the Anatta-nature of all phenomena.