The Bernoulli distribution is a discrete distribution parametrized by a "success" probability $p$. For a Bernoulli distributed random variable $x$, the probability mass function (pmf) takes a value of $p$ at $x=1$, and $(1-p)$ for $x=0$. A concise representation of the pmf is:
$$P(x;p) = p^x (1-p)^{1-x} \;\;\; \mbox{for} \; x=\left\{ 0,1 \right\}$$
The Bernoulli distribution is a special case of the binomial distribution with a single trial ($n=1$).