The idea is straightforward (no really!). Metamaterials can be made to behave like ordinary space with two dimensions of space and one of time. But they can also be made to behave like other types of spaces, with two dimensions of time and one of space, for example.
Smolyaninov points out that an interesting situation occurs when these two materials are place end on. If a time dimension is perpendicular to a space dimension, it simply hits a dead end. In other words, time runs out.