Speaking very broadly, structural equation modeling (SEM) is all about the covariance matrix between all of the variables used in the analysis. When we observe a bunch of variables, we can calculate an observed covariance matrix between all of the predictors. A covariance matrix is not a very parsimonious way to represent data, though, right? I mean, it's just a bunch of relationships between a bunch of variables.
When we create and test structural equation models, we try to simplify this picture without getting too far away from the original covariance matrix. We make a model that has a model implied covariance matrix. A lot of fit statistics measure just how close we get to the observed covariance matrix.
The goal is wanting to explain the data in a more parsimonious way without getting too far away from the observed covariance matrix.
Note that none of this deals with causality. When SEM was starting to be a thing, it was sometimes referred to as "causal modeling" or a technique for "causal inference." This is a total misnomer. You need three things for causality:
Covariation. The effect has to be related to the cause. This is what we can do in SEM.
Time precedence. The cause must come before the effect. This is not always the case in SEM; indeed, most of the time everything is measured cross-sectionally (i.e., at the same time).
Absence of alternative explanations. Making sure there are no other plausible explanations for the effect. In experiments, we often do this with random assignment and control over experimental materials.
There is no magic statistical technique to take cross-sectional evidence and infer something truly causal.
Structural equation models could have an indicator variable that is what experimental condition someone was in, and you could try to get at causality that way. But the main point here is that causality is not about a statistical technique. Statistics tell us about covariation, but methodological techniques help establish time precedence and absence of alternative explanations.
I did a bit of Googling, and it seems like this paper explains myths about SEM well. They make it a point to emphasize:
Lest there be any doubt: SEM does not aim to establish causal relations from associations alone.