Background
Kant distinguishes his position of critical philosophy from dogmatic or skeptical philosophy by invoking the distinction between transcendental idealism and transcendental realism. Kant succinctly defined transcendental idealism in this way:
[E]verything intuited or perceived in space and time, and therefore all objects of a possible experience, are nothing but phenomenal appearances, that is, mere representations, which in the way in which they are represented to us, as extended beings, or as series of changes, have no independent, self-subsistent existence apart from our thoughts.
A transcendental realist must, according to Kant, consider appearances - ie. the spatiotemporal objects of everyday experience - as imperfect shadows of a transcendent reality (Locke and Leibniz count as examples of this position). They make this mistake, Kant claims, because they consider space and time and objects alike, to be transcendentally real. The transcendental realist can only distinguish between objects (in general) and ideas. We cannot grasp ideas from objects, so we are always left to wonder whether our ideas really match (correspond to) the objects. This is why, Kant claims, the transcendental realist must be an empirical idealist, as the appearances of our senses are really just ideas in our mind on this position. Kant himself, being a transcendental idealist, can conversely consider the objects of our senses as empirically real, that is to say real within the necessary conditions of our faculties of thought and intuition. The transcendental idealist is thus an 'empirical realist'.
With regard to the adjective "transcendental" itself, Kant defined it in the following way when he used it to describe knowledge:
"I call all knowledge transcendental if it is occupied, not with objects, but with the way that we can possibly know objects, even before we experience them."

Transcendental idealism vs transcendental realism
Note that Xenophanes of Colophon in 530 BCE came up with something that could be considered an ancestor to Kant's epistemology: "And as for certain truth, no man has seen it, nor will there ever be a man who knows about the gods and about all the things I mention. For if he succeeds to the full in saying what is completely true, he himself is nevertheless unaware of it; and Opinion (seeming) is fixed by fate upon all things." (From Kathleen Freeman's Ancilla to the Presocratic Philosophers, Xenophanes fragment 34.)
Some interpretations of some of the medieval Buddhists of India, such as Dharmakirti, may reveal them to be transcendental idealists, since they seemed to hold the position of mereological nihilism but where minds are distinct from the atoms. Some Buddhists often attempt to maintain that the minds are equal to the atoms of mereological nihilist reality, but Buddhists seem to have no explanation of how this is the case, and much of the literature on the aforementioned Buddhists involves straightforward discussion of atoms and minds as if they are separate. This makes their position very similar to transcendental idealism, resembling Kant's philosophy where there are only things-in-themselves (which are very much like philosophical atoms), and phenomenal properties.

Dogmatic idealism
Some of Schopenhauer's comments on the definition of the word "transcendental" are as follows:
Transcendental is the philosophy that makes us aware of the fact that the first and essential laws of this world that are presented to us are rooted in our brain and are therefore known a priori. It is called transcendental because it goes beyond the whole given phantasmagoria to the origin thereof. Therefore, as I have said, only the Critique of Pure Reason and generally the critical (that is to say, Kantian) philosophy are transcendental.
Schopenhauer contrasted Kant's transcendental critical philosophy with Leibniz's dogmatic philosophy.
With Kant the critical philosophy appeared as the opponent of this entire method [of dogmatic philosophy]. It makes its problem just those eternal truths (principle of contradiction, principle of sufficient reason) that serve as the foundation of every such dogmatic structure, investigates their origin, and then finds this to be in man's head. Here they spring from the forms properly belonging to it, which it carries in itself for the purpose of perceiving and apprehending the objective world. Thus here in the brain is the quarry furnishing the material for that proud, dogmatic structure. Now because the critical philosophy, in order to reach this result, had to go beyond the eternal truths, on which all the previous dogmatism was based, so as to make these truths themselves the subject of investigation, it became transcendental philosophy. From this it follows also that the objective world as we know it does not belong to the true being of things-in-themselves, but is its mere phenomenon, conditioned by those very forms that lie a priori in the human intellect (i.e., the brain); hence the world cannot contain anything but phenomena.

P. F. Strawson
In Kant's Transcendental Idealism, Henry Allison proposes a reading in opposition to Strawson's interpretation. Allison argues that Strawson and others misrepresent Kant by emphasising what has become known as the two-worlds reading. This - according to Allison false - reading of Kant's phenomena/noumena distinction suggests that phenomena and noumena are ontologically distinct from each other and that we somehow fall short of knowing the noumena due to our subjective limitations. On such a reading, Kant would himself commit the very fallacies he attributes to the transcendental realists. On Allison's reading, Kant's view is better characterized as a two-aspect theory, where noumena and phenomena refer to different ways of considering an object. It is the discursive character of knowledge rather than epistemological humility that Kant asserted.