One of the great challenges facing physics today is to reconcile quantum theory and general relativity. Loop quantum gravity is an approach to this challenge that incorporates quantum theory into our description of spacetime from the very start. Quantum states of the geometry of space are described by "spin networks" - graphs with certain labellings of their edges and vertices. The theory predicts that geometrical quantities such as area and volume take on a discrete spectrum of possible values, and it explains the entropy of black holes by associating information to each point at which a spin network edge punctures the event horizon.
For more on this subject, start with these less technical papers:
Dig deeper with Carlo Rovelli's book, which is also available online:
Then, for more specifics on things mentioned in my talk, try these: