This notation is used often in MLE context to differentiate it from likelihood function and the estimation of the parameters conditional on data.

In MLE you do something like this:
$$\hat\mu,\hat\sigma|X= \underset{\mu,\sigma}{\operatorname{argmax}} \mathcal 
 L(X|\mu,\sigma)$$
$$\mathcal L(X|\mu,\sigma)=\prod_i f(x_i\in X|\mu,\sigma) $$

So, this notation emphasizes that you use the PDF $f(.)$ of the data set conditional on a candidate set of parameters to obtain the likelihood function $\mathcal L$. Then you pick the set that maximizes the likelihood as your solution $\hat\mu,\hat\sigma$. Thus, the solution is truly conditional on the data set $X$, while the likelihood is conditional on the candidate parameter set $\mu,\sigma$. That's why this notation is good for didactic purpose to show how the conditions sort of "flip" on left- and right-hand side.