The new material is made from graphene, which is the world's thinnest material. They took a sheet of graphene and blasted it with a camera flash or laser to deform it, causing several pores and cracks. This made the graphene sheet a great anode for lithium ion batteries because the lithium ions could cut through the pores/cracks to charge and discharge rather than run the entire length of graphene (which took much longer). This ultimately increased the power density. Source
Other research revealed graphene's self-healing capacity to "knit" itself back together. Hole-burning "metals" which were initially thought to damage sheets of graphene were later discovered to magically mend themselves. Source