The knight-piece symbolizes a mounted troop (such as calvary men or knights). It is capable of jumping pieces much like a horse could vault obstacles. Mounted soldiers could obviously travel greater distance then foot soldiers (pawns) hence the Knights movement of two up, however a mounted troop can't strike directly in front of themselves because the horses head is blocking them. So a horsemen would ride up slightly to the side of his target and strike them as they passed to the side hence the one over movement.
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