Kant's transcendental idealism explains the fact that experience presents us objects in a certain spatio-temporal order about which we can have some a priori knowledge by reference to a human capacity, our sensibility, through which alone we can become aware of objects. According to this explanation, space and time are then features only of objects as they appear to us. Confronted with this explanation, we are prone to ask what these objects are like apart from our sensibility, apart from how they appear to us (as spatio-temporal). Within Kant's own account, the concept of a thing in itself answers to this reflection: a thing in itself is any ordinary object (including event) considered apart from the spatio-temporal features it has by virtue of being an object for us (i.e. for beings with our human sensibility). Things in themselves are then the familiar objects of our experience, but considered in abstraction from their spatio-temporal features. And their existence is then no more problematic (if we accept Kant's explanation) than that of the objects of experience.

Moving beyond the Transcendental Aesthetic to the Transcendental Analytic, Kant also holds that the objects of our experience are products of mental synthesis performed by our faculty of understanding. This hypothesis is supposed to explain how we can have some a priori conceptual knowledge about the world of experience, for example the knowledge that every event has a cause. This explanation tells us what, according to Kant's account, things in themselves are: namely, products of the synthesizing activity of our understanding. We cannot be aware of this activity or its products as they are "in themselves", but only as they appear to us. On this reconstruction of Kant's view, things in themselves are then not wholly mind-independent entities that somehow affect the mind, but rather products of mental activity that appear to us a certain way. Here the relation of things in themselves to our experience of them as spatio-temporal is not a causal one.

Yes, Kant does disprove idealism elsewhere in the book: in the "Refutation of Idealism" added in the B edition. This Refutation seeks to show -- not: that there exist wholly mind-independent entities, but rather -- that we must take some of our experience to be of objects in space (which itself is "only" a form of human intuition).

Kant also uses the expression "thing in itself" in reference to various transcendental realist accounts he opposes. In those contexts the expression does refer to wholly mind-independent entities.