When I was running wild
Dragons breathing fire in the backyard at night
And it's so hard to breathe
Maybe the same old fears
What have we here
Don't bring me back
I'm holding heavy
And as we cross the line these fading beats have all been severed
Don't tell me our youth is running out
It's only just begun
Would you smile and turn away
It's like a bad dream that is too afraid to wake
And we're changing all the time
Maybe the same old fears
What have we here
Don't bring me back
I'm holding heavy
And as we cross the line these fading beats have all been severed
Don't tell me our youth is running out
It's only just begun
These fading beats
I'm holding heavy
And as we cross the line these fading beats have all been severed
Don't tell me our youth is running out
It's only just begun
A thousand dreams
A thousand dreams

This is a very beautiful song, one that I hold close to my heart and which seems to be the perfect soundtrack of a life I used to live.
I believe the lyrics are about denial to do with the pain of growing up past adolescence to the point where you finally have autonomy, but you no longer have freedom due to societal expectations of your responsiblities as an adult human being.
"Now I'm just chasing time with a thousand dreams I'm holding heavy" I believe this means the protagonist doesn't have enough time, but has many unfulfilled desires.
"And as we cross the line these fading beats have all been severed" By the time a goal has been accomplished, it no longer bears the same reward, perhaps?
"Don't tell me our youth is running out It's only just begun" Refusal to accept aging.
Just a guess, I most probably am wrong. Still, stunning song.
I couldn't said it better
I couldn't said it better

I think thing this song is about having a lot of goals and desires in life but fearing that you won't have enough time or the chances to fulfill all of them.
"Now I'm just chasing time With a thousand dreams I'm holding heavy."

Great song!