Our perception of context is a compound phenomena (sankhara) fabricated or assembled (sankharonti) by the mind from multiple individual thoughts: what is this, where is this, what am I doing, what is my goal, where I came from, etc. As you can see thanks to meditation, mind does quite a lot of work to assemble what it calls reality.
This works the same way in the waking state as in a dream, except the waking state gives you more clues, but the effort of fabrication is the same.
This insight, that reality is a fabrication we make, is almost more important than meditation itself. It gives us new frame of reference in which we can finally choose how we perceive reality, by choosing what we turn our attention to ("guarding the doors") and gluing it together with power of will (loosely: faith, determination, mindfulness, concentration). So we no longer have to get stuck in negative thinking of the six kama-dhatu worlds. Instead, we can feed our mind with positive information, until it gets strong and healthy (first 3 jhanas). Once our will gets strong we can be free to choose our reality on case-by-case basis (4th jhana and beyond).
You say "awareness is an important concept in buddhism" -- but what is this "awareness" really? Aren't we always aware of something, even when we are obsessed with desire or negativity? In Buddhism, mindfulness (sati/smrti) is not just passive awareness of whatever worldly activity we may be performing at the moment, it is a mastery over one's context. We can see this power developing through five levels (panca bala): faith, effort, mindfulness, concentration, and wisdom.
- At entry level mindfulness starts as faith in the live tradition. Inspired by an encounter with Sat-Dharma, your mind gets the bug of Buddha-fever. Unable to resist the urge to find out more, you keep thinking about mysterious Dharma.
- At beginner's stage mindfulness means applying effort to constantly check one's current physical, verbal, and mental activity against the context of Eightfold Path. Is my mind presently biased by attachment? Is my current action motivated by egoistic intent?
- The next level is when staying always mindful of the context of Dharma becomes automatic and no longer requires effort, which means one is now always operating in the phenomenological context of the Four Right Efforts.
- At middling level mindfulness grows into concentration (samadhi) which means we can now design, assemble, and maintain any context we choose.
- Finally, at advanced level mindfulness becomes wisdom (prajna), which means seeing all contexts at the same time and freely juggling their elements as required by a situation at hand.