If X denotes the number of successes in n trials, then X is a random variable which can take the values 0, 1,........, n. Since in n trials, we may get no success, one success, ........., n success. Total probability is unity. Since the probability are the successive terms in the binomial expansion (q + p)$^n$, it is called the binomial distribution.
Binomial distribution is also known as Bernoulli distribution after the Swiss mathematician James Bernoulli who discovered it in 1700 & was first published in 1713, 8
years after his death.