As we increased the surface area means that more places where wood can turn into flame (Where heat, fuel, and oxygen all are present in the same place at the same time). The mass of the small particle is such that the entire article can be heated to ignition temperature.
An iron rod will not burn as it has relatively very less surface area per unit mass but iron fillings with more surface area per unit mass can burn in air and get converted into air oxide. Wood has a lot of surface area and therefore has more contact with oxygen, making them easier to burn.