Higher Order Theories of Consciousness take a common account for consciousness based on higher-order representations of conscious states. For the sake of clarity and as a preliminary explanation we could just say that Higher Order Theories (HOT) try to model consciousness as a higher-order thought about a thought.
As always, the most controversial dimension of consciousness to be explained is the phenomenal or subjective experience (Qualia). i.e., the famous what-is-it-like-ness as described by Nagel (1974) in terms of what would it be like to be a bat. Higher Order Theories try to explain phenomenal consciousness in terms of higher order representations. Then, we have the access dimension, which is a much more comfortable concept in terms of computability. From the point of view of accessibility, we can say that there are some mental states that happen to be accessible to consciousness, which means that we are actually aware of these states.
Higher Order Theories of consciousness can be framed within cognitive science as the focus on the cognitive level of description in order to explain phenomenal consciousness. In other words, HOT theories reject the idea of (phenomenal) consciousness being a fundamental property of the mind’s substrate. Instead, they consider certain representation processes as the source of consciousness production. Concretely, those representations which are higher order thoughts or beliefs of a mental state.
The usual way to differentiate between conscious and unconscious mental states is to consider that the first are those of which we are aware. According to Higher Order Theories, this is to say that conscious states are those that are the object of some sort of higher representation.