This refers generally to statistical procedures that utilize the probit function. The primary example of this tag is probit regression where the probit transformation of the parameter p of a Bernoulli distribution is used as a link.
The probit function is the inverse standard normal cumulative distribution function. That is, it takes in a probability and outputs a z-score. One important use of the probit is as a link function for the binomial distribution in the Generalized Linear Model.
For GLMs, we motivate the probit link function as follows:
Instead of modeling the response $Y$ directly in terms of $X$, we can model it through a latent variable
$$Z = X^\top\beta - \epsilon,$$
where $\epsilon_i \sim F( \cdot)$, i.i.d from some distribution with cdf $F$. In binary regression, we could classify observations, $Y_i$ as class 1 if $Z \ge 0$ or class 0 otherwise. So
$$P(Y=1|x) = P(Z \ge 0 ) = P(X^\top\beta - \epsilon \ge 0)$$ $$=P(\epsilon \le X^\top\beta) = F(X^\top\beta)$$
When $F$ is a Normal cdf, then the expression above is $\Phi(X^\top\beta)$, corresponding to a probit regression.
'Probit' is short for probability unit. The idea was originally proposed in the 1930s and predates the (now more common) logistic function.
