The Buddhist idea of emptiness is often misunderstood as "nothingness" which is why Buddhism has been mistakenly spoken of as nihilistic.1 When emptiness is mentioned in the context of Buddhist sutras what is meant is a lack of a permanent, unchanging essence.
To paraphrase an example often cited by Thich Nhat Hanh; when one considers a piece of paper deeply, one sees not just the piece of paper but all constituents of the paper that caused it to come into being. That would include the tree that the wood came from, the clouds that provided rain, the sun, the logger, etc, until eventually all of everything is included in the paper (this same idea can be used to illustrate interdependent arising). The paper is entirely composed of non-paper elements, so the essence of the paper is empty of paper. Using this view on the Self, one can see exactly the same thing. The self is composed of experiences and matter that are all constantly changing and are not the self itself so are thus empty.