What is a Probability Mass Function?
If $X$ is a discrete random variable, we can list the values it takes.
If $x$ is one of these values, the probability $X$ takes that value is $\mathbb{P}(X=x)$.
This defines a function from $x$ to $\mathbb{P}(X=x)$; the probability mass function of $X$.
The PMF of $X$ gives its “personality”, or typical behaviour. It used to uncover further features of $X$ as a random variable, such as its expectation.