This is similar to a Birch reduction, but without ammonia. In this case, the first thing that happens is the Li delivers an e- to the biphenyl system. This allows for the electron to be "solvated" in organic solution similar to how it is solvated in ammonia. From the biphenyl radical, the electron is transfered to the phenyl group of the phenyl thioether. This can then fragment to liberate a thiophenol radical and a carbanion. The carbanion can then eliminate out the carboxylate adjacent to it, forming the olefin. The thiophenol radical can then be reduced by a second equivalent of the lithium and you're done.
Does that make sense?