Holographic entanglement entropy is part of an expanding dialogue has opened between string theorists and physicists in a variety of other fields, eg, condensed matter and nuclear physics. Holographic entanglement entropy also provides an interesting window into the suggestion that quantum entanglement plays an essential role in the emergence of spacetime geometry in theories of quantum gravity. In this lecture, I will review some of the basic aspects of entanglement entropy and holographic entanglement entropy. I will also describe how holographic entanglement entropy leads one to consider associating entanglement entropies with general regions of spacetime in quantum gravity. Finally, I will discuss some recent work to examine this conjecture more precisely in the context of the AdS/CFT correspondence.