Suppose you flip a coin 6 times and want to know the probability of obtaining 4 or more heads in the 6 tosses.  This is a binomial distribution problem with n = 6, x = 4 and p = .5.

Suppose you flip a coin and want to know what the probability that the first head you obtain is on the 3 third roll. This is a geometric probability distribution problem.

Whenever you want to know the probability of some event occurring for the first time on the xth trial, you have a geometric probability distribution problem.