Kant's project in the Critique of Pure Reason is to investigate the limits of human reason. One of his most important conclusions is that we do not have direct access to true reality, that we, as humans, have to deal with appearances alone. This is for him a result of the nature of our perception, since he considers it to necessarily entail that we could not in fact be perceiving the world in an unrestricted manner. His doctrine of transcendental idealism tries to combine a coherent philosophical position with many of the intuitions about our experience that we possess. For instance, despite claiming that we only have access to the phenomenal world, he also maintains that we can have objectivity. He asserts that the spatio-temporal world is a result of our mode of cognition, and thus common to all humans, and attempts to prove this. However, he also asserts that it is not the only possible mode of cognition, and that we can never expect to be able to perceive things in themselves. His theories are therefore a combination of transcendental idealism and empirical realism, which for him is the corollary of transcendental realism.
Kant distinguishes between two standpoints in his theory: the transcendental standpoint, where the perception is unbounded, and one can perceive things in themselves, and the empirical standpoint, which is the perception that entities have of the world. Whilst he does not deny the possibility of these two standpoints coinciding, he does deny its possibility in our case. As humans, we can never perceive things as they are, only as we intuit them. He offers several arguments for this, which I will look at later, but the result is the separation of the world into two realms, the phenomenal and the noumenal. The noumenal realm contains objects as they are in themselves, and, depending on your interpretation of Kant, the phenomenal realm is either a realm dependent on the noumenal one that we are able to perceive, or is simply a fiction that we create as we perceive the noumenal realm. I find the second interpretation to be more reasonable, interpreting Kant as saying that there is one existing world, in which there are entities in themselves (noumena), but our perception is incapable of providing perfect perception of these entities, and we can only intuit imperfect versions of them (phenomena), due to our limitations as humans. This 'two aspect' view can be summarised by saying that there is one existing world which can be perceived in two different manners, either the transcendent one, where one is able to see the world as it actually is, or the empirical one, where one obtains a consistent but imperfect perception.
However, even though we do not have transcendentally true perceptions of the world, we are able to call our perceptions objective at times. This is because the manner in which we perceive the world is a necessary element of being human, and is thus common and consistent to all humans. To some this is an insufficient attribution of the term objective, but it seems to me that without achieving a position equivalent to God's, one could never achieve the true objectivity in its strongest sense, and we still need to differentiate between different levels of accuracy in our limited empirical standpoint, so why coin a new phrase when there already exists the objective / subjective distinction.
The next definition that must be discussed is that of transcendental idealism and all its cohorts, before then going on to fully answer the question by seeing which categories space and time fit into. For Kant there are two possible modifiers to each of the standpoints: realism and idealism. Roughly speaking, realism is to say that the entity of which one is speaking has the form it appears to, idealism is to say that it does not. Therefore, to say something is empirically ideal is to say that it is phenomena unrelated to noumena, in other words it is pure phenomena, it has no substance. Therefore hallucinations, dreams and mental images are empirically ideal. These are the essentially unimportant by-products of perception. Empirical realism on the other hand is the class which Kant believes most objects inhabit for us. Since we can only deal with the phenomena, and, as already shown, we may legitimately term them objective, they can be said to be empirically real. We are unable to experience them in any different manner, so they are, for us, necessarily as they are, and thus empirically real. Transcendental realism is the view which Kant is working against, the view that what is perceived is what is there. One can typify the view by saying that transcendental realists would have us perceiving the noumena accurately, and thus no use for phenomena, except perhaps for hallucinations etc. Kant considers this view to be fundamentally misguided, but we will come on to the arguments for this later. The most important category for Kant is that of transcendental idealism. This category contains objects which really exist, but which we do not perceive as they really exist. Thus, to say that something is transcendentally ideal is to say that we can only perceive its appearance, not its true constitution.
For Kant the spatio-temporal world is a necessary product of the human condition, that is to say that all humans will experience things in space and time. Since, as we have seen, that qualifies as objective for him, it means that space and time are empirically real. For us, there is no possibility of experiencing things outside space and time (except for internal states, which are only in time), and they therefore are real in the appropriate sense. However, since he claims to have demonstrated that space and time are not necessary elements of any possible experience, they cannot be transcendentally real, and the spatio-temporal world is thus also transcendentally ideal.