At its core Lonergan's critical realism is an account of human knowing. His magnum opus, Insight, is 720-page work devoted to describing what we are doing when we have insights and then working out the entailments of that description (his later major work, Method in Theology, is really just working out the implications of the matters explored in Insight for the specific discipline of theology). That is Lonergan's genius: he does not begin by asking "How should we go about having insights?" but rather "How do we go about having insights?" In Insight he identifies a recurrent structure present in every instance of human knowing: we attend to the data, we get an insight from the data, we judge whether that instance is true or false. The "proof" for this structure is that one cannot argue against it without employing it (try: you will have to attend to the data that is the text of Insight; you would have to have insight into what Lonergan is arguing; you would have to judge as true your insight into what Lonergan is arguing; then, still attending to the data, you would have to have insight into why Lonergan is mistaken; then you would have to judge that insight as true). Insight is 720 pages of hermeneutic-y goodness devoted to figuring out 1) the conditions that make it possible for one's judgments regarding truth and falsity to correspond with the world of being and thus themselves be true (i.e. I can judge an insight to be true when it is fact false, and vice versa, thus rendering my judgment false) and 2) what the very fact of knowing says about the world in which we live (i.e. he's working out a metaphysics from his basic epistemic observation) and also how it opens up the possibility of thinking responsibly about how to live in said world (i.e. the question of ethics).
The above accounts for why Lonergan (and New Testament scholar Ben Meyer after him) can describe his account of knowing as a "critical realism." On the one hand we construct our knowledge of the world--our reality--from judgments rendered upon insights into the data of the world; hence it is critical. On the other hand, when we carefully and diligently attend to the conditions necessary for rendering sound judgment the reality that we construct will correspond as close as conceptually possible to the world; hence it is a realism. Thus a critical realism.