The Poisson distribution represents the probability of a provided number of cases happening in a set period of space or time if these cases happen with an identified constant mean rate (free of the period since the ultimate event). Poisson distribution has been named after Siméon Denis Poisson(French Mathematician). 
Many probability distributions can be easily implemented in R language with the help of R’s inbuilt functions.

In R programming, the Poisson distribution is a probability distribution that describes the likelihood of a given number of events occurring in a fixed interval of time or space. It is often used in modeling situations where events occur randomly and independently over time, such as the number of phone calls received by a call center in a given hour or the number of cars passing through a tollbooth during rush hour.

The Poisson function in R is used to calculate the probability of a certain number of events occurring in a given time or space interval, based on a specified rate parameter. The syntax for the Poisson function in R is as follows: 

dpois(x, lambda)

Where "x" is the number of events, and "lambda" is the rate parameter. The function returns the probability of "x" events occurring, based on the Poisson distribution with a rate parameter of "lambda".

In addition to the probability density function, R also provides other functions related to the Poisson distribution, such as the cumulative distribution function, quantile function, and random number generator.

Overall, the Poisson function in R is a useful tool for modeling and analyzing situations where the occurrence of events follows a Poisson distribution.