When we increase the surface area of an object, more atoms are exposed. Since more atoms are exposed, the atoms can react faster, and this is why the rate of a reaction increases when the surface area increases.
For example, lets say we want to heat a potato. If we just put the whole potato in the microwave, it will take a long time for the potato to get thoroughly heated. However, if we chop the potato into smaller pieces, we will observe that it gets heated much faster. This is because we increased the surface area of the potato, which resulted in more potato atoms to be exposed to the heat, and caused the reaction to be faster.
