Until they become conscious they will never rebel, and until after they have rebelled they cannot become conscious.
The sentence is describing how the people are "caught" in a loop that they cannot get out of.
Until they become conscious they will never rebel
They can't rebel now, because they are not conscious yet. (People who are unaware of a good reason to start a rebellion generally won't rebel).
and until after they have rebelled they cannot become conscious.
They will stay in their "unconscious" state until a rebellion breaks out.
Ergo, they are stuck.
It's worth noting that unconscious in this context means "unaware of their miserable existence, as if in a stupor." It doesn't mean the people have fainted or passed out.
NOAD defines it as:
conscious (adj.) having knowledge of something; aware: we are conscious of the extent of the problem.