What is meant by categorical distribution?

The categorical distribution is the generalization of the Bernoulli distribution to a fixed number $2 \le k$ of outcomes.

Equivalently, it is the special case of the multinomial distribution where the number of “choices” $n$ is fixed at one.

Therefore, it has pdf:

$$\prod_{i=1}^k p_i^{x_i} \qquad\text{(where $0\le p_i$ and $\sum_i p_i = 1$)}$$
over the support
$$x_i \in \{0,1\}$$
where
$$n \triangleq \sum_{i=1}^k x_i = 1.$$

In summary, Bernoulli has $k=2, n=1$, binomial has $k=2, n\ge 1$, multinomial has $k\ge2, n\ge1$, and categorical has $k\ge2, n=1$.