"Well dreams, they feel real while we're in them, right? It's only when we wake up that we realize how things are actually strange. Let me ask you a question, you, you never really remember the beginning of a dream, do you? You always wind up right in the middle of what's going on."
I watch a lot of motivational videos and speeches. When Eric Thomas, Zig Ziglar, Jim Rohn, and Les Brown speak of dreams, they're usually referring to something different than the dreams of Inception.
When I heard this line being quoted at the beginning of a song, I thought: What if the dreams Cobb is referring to had nothing to do with sleep but, rather, were the long-term vision you have for your life?
In that case, he's saying that "dreams feel real while we're in them". Our dreams are the manifestation of our innermost desires, so when we accomplish them, of course, they don't feel foreign. However, there will always come a moment when you "wake up" and "realize how things are actually strange", that I-never-imagined-I-would-actually-end-up-here moment. You'll probably smile and ask yourself, "How did you get here?"
In order to make your dreams come true, you have to put in some SERIOUS WORK. You will sacrifice sleep, comfort, and some relationships for it! There WILL be setbacks and plenty of obstacles to overcome. The emotional, physical, and spiritual toll will all but kill you.
Now, one of the brain's coping mechanisms is known as psychogenic amnesia - memory loss due to situations of extreme stress and emotional trauma. This can be a good thing; you don't want to be constantly reminded of your pain as you work your way toward your dreams, right? This memory loss allows you to put some of your sacrifices away in your mind and focus on positive things.
So, if you dream so big that you have to work so hard and go through so much to achieve those dreams, then, once you finally do it, you will be rewarded with a state of presence that forces you to be "right in the middle of what's going on". Happy - enjoying the fruits of your hard labor without a care for "the beginning of the dream". Food for thought.