Is there an intuitive way to explain the forumla ?

For example in the binomial distribution with n trials & probability of sucess p you can see that to get r sucesses you must also have n-r failures and the trials are independent so this probability is p^r x (1-p)^n-r, and then you don't care about the order so that's where the n choose r comes in...

But is there a way to explain the poisson formula? Where did it come from?