Izaya Orihara uses this Shogi board to plan out what he is going to do to Ikebukuro, using pieces from different games in a way that only he and apparently Shingen can understand. Every piece represents a person that has managed to catch his interest or that has an important role to play in his plans, changing their position on the board depending on what they do.
There are many other pieces, however, the people Izaya assumes they are were never revealed; mostly pawns, which could represent humans or collateral damage. In the beginning of the Yellow Scarves Arc Izaya lights the board on fire as he imagines Ikebukuro suffering the same fate due to his plan. He gets another board by the end of the Yellow Scarves Arc.