It means that I will cease to exist, and very well that could happen in a very 'real' way, even with my consciousness - I am no more. My awareness/self is wiped out of the universe. I used to be more alarmed at this, until I realized that it would be no different from sleep - each night when I sleep I am effectively non-existent, as if I died in my sleep I would have no idea. Just as when I wake up I effectively have no idea what happened while I was sleeping.. because I wasn't aware of any of it.
But it's also possible that my consciousness will continue on in some way. I won't know until it happens, or when it happens, nothing will happen other than what I said above.
Basically I don't have any beliefs regarding what will happen after I die, because I don't think I'm in a position to really know. Of course I think it would be rather nice for my consciousness to continue ever on, in some capacity/form, but I'm also not banking on that. What happens happens.
I have had the same thoughts, the same comparisons to sleep, etc. There's a reason that sleep is seen as a mini-death and that death is sometimes referred to as sleep. I used to have trouble when I was young going to sleep, because I did not know if I would wake up again.
I have a hard time saying I believe in specific details that I cannot confirm are true, even if they are palatable. Religious beliefs seem to be that way for me. I use patterns in religious systems to help me determine how to live and to help me define my hopes and joys, but the reality is that I don't know what is true and what is not in terms of the specifics; death will provide a final answer that unfortunately at that point in time will no longer have meaning. All that matters to me now is how I live now, not what happens after death. (I don't even understand people who can focus on eternal reward as a motivator, and so loudly proclaim something that might or might not be true.) When I get there, then I'll be subject to what it is, and if I'm still conscious, then it'll be something new to work through.
Why is mortality something to be hurdled? Why would perpetual life necessarily be a reward?
I don't know why it is looked at that way. Sometimes eternal life could be seen as a curse, as much as a suffering eternity here on earth would not be heaven but hell.
My mind leaps through many patterns. I remember the end of "Insomnia," where Detective Dormer has probably lost his life's work and been mortally wounded, and now he's ready to rest and just says, "Sleep, Let me sleep," rather than being saved. (See "Awake" from "Sucker Punch" too.) Sometimes I've felt that way; even when life is good, the pain of some experiences still lingers and leaves me grateful at the thought of releasing all that and finally being at peace. It's good to finally be able to lay down your burden and find a respite from the unendurable grief, there at that end of all things.
Also reminded of the end of Billy Joel's "Lullaby" to his daughter:
"...Goodnight my angel now it's time to dream
And dream how wonderful your life will be
Someday your child will cry and if you sing this lullaby
Then in your heart there will always be a part of me
Someday we'll all be gone
But lullabies go on and on
They never die that's how you and I will be"