An integer-valued random variable $X \sim \text{Binom}(n,p)$ if
$$ P(X = x) = \binom{n}{x} p^x (1-p)^{n-x}, \qquad \qquad \text{for } x \in \{0, 1, \ldots, n\}.
$$
The mean and variance of $X$ are
$$ E(X) = np, \qquad \text{Var}(X) = n p(1-p). $$
Images of the probability mass function (pmf) for different choices of $n$ and $p$ are shown below.
See the probability calculator to explore more parameter choices
Here is a great video introduction from Primerr to help your intuition.
https://www.youtube.com/watch?v=6YzrVUVO9M0
The Binomial distribution is perhaps the most natural of all probability distributions to articulate. In a binomial experiment there are a sequence of $n$ independent (meaning that the outcome of one trial does not affect the outcome of others) and identical trials each with a probability $p$ of success.
Classic examples of binomial experiments involve counting the number of heads among $n$ coin flips $(p = 1/2)$, counting the number of ones among $n$ rolls of a fair die ($p=1/6$ if it is a six-sided die), and whether the top card on a “well-shuffled” deck is an ace $(p = 1/13)$.
We also often model real-life scenarios as binomial experiments even when we know there is likely some small degree of non-independence (or correlation) or non-identicality among the trials. For example, suppose a basketball player attempts 20 shots at the free throw line (which is an uncontested shot 15 feet away from the goal). Obviously there are many ways that the attempts are not identical or independent. Some players get into a better routine after a few attempts, so the probability of success might actually increase as the experiment proceeds. On the other hand, the player might get tired, which would cause the success probability to decrease. Either way, these would violate the assumption that the attempts are identical. BUT, we often make the assumption that they are close enough to identical that the binomial model is useful. Similiarly, the outcomes of the attempts may not be independent. If the player becomes more confident after she makes a shot, that might improve her probability of making the the next one successfully. We would say that, for her, successive outcomes are positively correlated.
The key is that there is no such thing as a perfect experimental set up. Our job as probabilistic thinkers is to be clear about what assumptions we are making and whether the deviations from these assumptions are substantial enough that they might undermine our model.