Binomial - Random variable X is the number of successes in n independent and identical trials, where each trial has fixed probability of success.
Hypergeometric - Random variable X is the number of objects that are special, among randomly selected n objects from a bag that contains a total of N out of which K are special. If n is much smaller than N then this can be approximated by binomial.
Poisson - Random variable X counts the number of occurrences on an event in a given period, where we know that the concurrences has an average of \lambda for any period of that length, independent of any other disjoint period.