How does a particle interacts with another particle. Have you ever thought, how does one electron get to know presence of other? Obviously there must be some information exchange between the particles. This information exchange takes place with the help of exchange of some elementary particles, which are called force carriers and force between two particles should depend on number of force carriers reaching either of the particles. Since particles are essentially point objects so force carriers starting from one particle and reaching other should be inversely proportional to square of distance between the particles. 
Yukawa explained the behavior of force carriers for strong nuclear forces. According to his theory strong forces are carried by carriers which decay with time. So according to Yukawa theory the intensity of strong forces should not only diminish with distance as the inverse of square of distance but also get diminished because force carriers decay with time. Number of carriers remaining after time t is proportional to $e^{-\lambda t}$ where $\lambda$ is decay constant.