As well as being an amazing song, I think it fits the Fallout story very well. Let me give you some lyrics:
I don't want money or a thing
For what I was and what I am and what I'll ever be
I don't need to be overground
I don't need to give away my life or make a sound
All I ever wanted was the thing I couldn't find
This refers to life in the Vault.
I don't wanna make a judgment call
Take a stand or make demands or try to please you all
All I wanted was the truth and that I couldn't find
Refers to how individuality is mostly crushed under the overseer. Especially 101.
Oh I tried to get away - run away, far away
But my shadow followed me - every place, kept my pace
Well I don't belong anyway
Well I missed my call - what a shame
Refers to leaving the Vault. Mostly Fallout 3 on this one.
I don't want much of anything
Everything I got I earned through pain and suffering
I don't want you numberin' my days
I don't want you trying to immortalize my name
All I ever wanted was a little peace of mind
Refers to how 101 and the Vault Dweller are treated as heroes (usually) upon leaving the Vault.
And what I have you can't touch or see
All I have I got from God and that's all I need
All I ever really wanted was to stay inside
This could refer to the Vault dwellers seeing the Enclave as a God-like authority.
Well I tried to believe I was freed - in the lead
Yeah, I thought I could succeed - but it's not my need
Something there was in my way so I stayed - stood in place
Where forever I'll remain - it was not my way
Refers to how, in the end, both 101 and the Vault Dweller eventually die.