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By decreasing the particle size of a reactant, we are increasing its surface area. The greater the surface area, the higher the chance of collisions, thus the faster the rate of reaction. The smaller the particle size the faster the reaction.

Think of a cube where the length of every side is 2 cm.

The area of one face of the cube will be 2 x 2 = 4 cm^2.

The cube has six faces, so the total surface area is 4 cm² x 6 = 24 cm².

We could cut that cube horizontally and vertically along each face so that we have eight smaller cubes.

Each of the small cubes has a face area of 1 cm x 1 cm = 1 cm².

The six faces give a total surface area for each smaller cube of 6cm².

There are eight cubes so the total surface area is 6 cm² x 8 = 48cm².

This video clip has demonstrations with charcoal, gunpowder and steel wool that show the effect of particle size and concentration on reaction rate.