An awakening is the act of waking up from sleep. It can also refer to other forms of new or sudden consciousness.
When you've been asleep, whether at night or during a nap, you wake up and regain consciousness. This is known as an awakening. However, this word is often used for more dramatic things than getting out of bed. Having a religious epiphany is an awakening. Deciding to get married could be considered an awakening. Any time you realize or accept something important and life-changing, it can be called an awakening, because it's almost like you were asleep before.