The quick-and-dirty explanation is that the E8 "object" is a nasty-ass shape that exists in 248 dimensions, and which is notable for various reasons that only mathematicians can really grasp fully, but can be understood by the layman as pertaining to the concept of symmetry. It was discovered in the 1890s, but due to its size was never fully computed until a couple of years ago (the solution is a massive matrix of polynomials taking up 60 GB of storage). Oddly, various aspects of the E8 solution were reminiscent of formulae in the Standard Model, and Lisi has managed to come up with a coherent explanation of why this is. Various aspects of the E8 object's structure appear to explain formerly mysterious facts, such as why elementary particles are grouped into their various families. They also suggest new and undiscovered particles, which may give this theory a very clear set of test cases if it survives that long.
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