The "awake, and arise" idea is one that is found both in the temple ceremony and the scriptures (e.g. Isaiah 51:17; 2 Nephi 1:14; Moroni 10:31; D&C 133:10). It is a pairing of two ideas that is sometimes conflated and oversimplified into one. We should understand them as two distinct things which ought to be engaged in tandem, but can also be engaged singly with unfortunate results.
To awaken is to transition from sleep to consciousness. When we are asleep, we are oblivious to the real world. Most often, we are engaged in a dream world which rarely–if ever–matches the real, waking world in which we slumber. In the dream world, things can appear wildly different than reality, yet we accept them as perfectly normal. Perhaps you can fly, perhaps you "know" different people than in reality, perhaps even your own moral compass and manner of being is nothing like who you are when awake. Yet while asleep, we accept it as all being reality.
Upon awakening, we realize that the dream world–which moments before we thought was reality–was in fact a dream. What we saw, what we thought we understood, we realize in the waking world was incorrect. We cannot fly about, we don't know those people, we aren't actually that way. That was a dream world, constructed for us to engage in while we slept, but now we are awake. Our waking eyes observe the world in which we presently reside, and we see that we must think and act differently in this world than in the dream world. It is a wholly different world view.
After we are told to awake, we are told to arise. But we could choose otherwise. We could go back to sleep. Finding the enticement of the real world insufficient, we can close our eyes to it and re-enter a construct with rules and elements out of alignment with what we've seen is reality. We can again forget the real world and dive into the darkness and dreams. But we will have to account for our choice to return to slumber when we are supposed to awaken.
Alternately, should we arise without having awoken, we find ourselves sleepwalking. If you have ever observed sleepwalkers, you have seen that the "reality" with which they believe they are engaging doesn't quite match the real world in which you are observing them. They may get some things correct, stepping around a table rather than running into it. But they will also mumble nonsense, like about breakfast cereal chasing them around the room, or climb under the kitchen sink because it will help them escape a dinosaur. To the awake, it is obvious that they are watching the person act foolishly due to their inability to distinguish reality from the dream world, being asleep. They say and do things that they would recognize as ridiculous if they were awake and could see themselves. But they are not, they are asleep.
If we awake and then choose to arise, we engage in works that account for our waking observations as being real. We don't reject the real world as too uncomfortable, too out of harmony with our ideal world, too unlike our dreams to accept and engage. Upon waking and recognizing that we are laying down in a bed, we cast off the blankets and arise to engage the waking world. The dream world is no longer an influence. We know better than to jump out the window and expect to fly. We don't treat the dream world as real anymore. We accept our "newly" informed reality since leaving behind the dream world, and we engage it.
Awake, and arise!