What is consciousness?

There may be more clarity in addressing the relationship between consciousness and some other attribute like awreness, than describing consciousness on its own.

Baghavad Gita:
makes several references to spirit as consciousness. Examples:
The individual soul (Jiva, Jivatma) in the body of living beings is the integral part of the universal Spirit, or consciousness. The individual soul associates with the six sensory faculties ¾ including the mind ¾ of perception and activates them. (15 .07).

I am the Vedas, I am the celestial rulers, I am the mind among the senses, I am the consciousness in living beings. (10.22)

Spirit (or Consciousness) is said to be the cause of experiencing pleasures and pains. (13.19-20)

Advaita

"The manifold universe is, in truth, a Single Reality. There is only one Great Being, which the sages call Brahman, in which all the countless forms of existence reside. That Great Being is utter Consciousness, and It is the very Essence, or Self (Atman) of all beings."[Feuerstein summary).

Consciousness is Brahman (Upan's and Rgveda)

Buddhas Lists.pdf

It is the evolution of the human consciousness through  

introspection. The consciousness becomes gradually conscious of itself, and thereby loses the

delusion of existence. It is experiencing experience instead of existence.

The twelve parts to Dependent Origination are: through ignorance conditional volitional or

willful actions or kamma formations take place. Through willful actions there isconditioned consciousness, then conditioned mental and physical phenomena, then the six senses(five physical senses and the mind), then conditioned contact, then conditioned sensation, then conditioned desire, then conditioned attachment, then the process of becoming, conditioned birth, then decay, death, sorrow, pain, etc., and then the process starts again.

This koan is difficult because we do know that all living beings have buddha-nature, that is, the capacity for insight and enlightenment. All living beings are sentient beings with consciousnessand experience pleasant and unpleasant emotions, feelings, and sensations.

The Heart Sutra works to just that end of seeing beyond the opposites, beyond dualism:Form is only emptiness, emptiness only form. Form is no other than emptiness, emptiness no other than form. Feeling, thought, and choice, consciousness itself, are the same as this.

The Five Aggregates 

People get caught in the dualistic trap, which is easy, and insist that we must either exist or we do not exist, it can not be both ways. In Buddhism the concept is no-self, but there are the five aggregates:

1. Matter 2. Consciousness 3. Feeling 4. Perception and memory 5. Mental formations

Hinduism (wiki)

idea that Brahman is "Sacchidananda" (Truth-Consciousness-Bliss). 
Advaita: Georg Feuerstein summarizes the advaita realization as follows: "The manifold universe is, in truth, a Single Reality. There is only one Great Being, which the sages call Brahman, in which all the countless forms of existence reside. That Great Being is utter Consciousness, and It is the very Essence, or Self (Atman) of all beings."^[17]

Lankavatara Sutra

I wish to see the Blessed One again, who has all the disciplinary practices at his command, who has turned away from the practices of the philosophers, who is born of the state of realisation in the inmost consciousness, and who is beyond [the dualism of] the transformed and the transforming.

Lord of Lanka, beings are appearances, they are like figures painted on the wall, they have no sensibility [or consciousness].

The reasons whereby the eye-consciousness arises are four. What are they? They are: (1) The clinging to an external world, not knowing that it is of Mind itself; (2) The attaching to form and habit-energy accumulated since beginningless time by false reasoning and erroneous views; (3) The self-nature inherent in the Vijnana; (4) The eagerness for multiple forms and appearances. By these four reasons, Mahamati, the waves of the evolving Vijnanas are stirred on the Alayavijnana which resembles the waters of a flood. The same [can be said of the other sense-consciousnesses] as of the eye-consciousness. This consciousness arises at once or by degrees in every sense-organ including its atoms and pores of the skin; the sense-field is apprehended like a mirror reflecting objects, like the ocean swept over by a wind.

Nisargadatta

There is consciousness in which everything happens. It is quite obvious and within the experience of everybody. Ultimately even the observer you are not. You are the ultimate potentiality of which the all-embracing consciousness is the manifestation and expression.
Consciousness needs a vehicle and an instrument for its manifestation.
it is only so from the mind’s point of view, but In fact the entire universe (mahadakash) exists only in consciousness (chidakash), while I have my stand in the Absolute (paramakash). In pure being consciousness arises; in consciousness the world appears and disappears. All there is is me, all there is is mine.
I see the world as it is, a momentary appearance in consciousness.
If you trust me, believe when I tell you that you are the pure awareness that illuminates consciousness and its infinite content. Realise this and live accordingly.

RAMANA
Existence or Consciousness is the only reality. Consciousness plus waking we call waking. Consciousness plus sleep we call sleep. Consciousness plus dream, we call dream. Consciousness is the screen on which all the pictures come and go. The screen is real, the pictures are mere shadows on it. http://www.sriramanamaharshi.org/teachings.html

The Buddhist Unconscious
The work thus first presents the multivalent conception of consciousness (

vijñana) within the early teachings of the Buddha, and then demonstrates how the Abhidharma emphasis upon momentary and conscious processes of mind was widely understood to make the continuity and multidimensionality of consciousness problematic in several crucial ways.