Explain the doctrine of eternal return.

This is going to be difficult.  The doctrine of eternal
return essentially configures time in a cyclical pattern and not a linear one.  In this
light, the life we lead, we end up leading repeatedly.  If time and space are indeed
infinite, then the implication here would be that there would invariably be repeating
patterns to existence and consciousness.  This means that we, as human beings, are not
necessarily living a life that is completely and absolutely authentic.  Rather, figments
and fragments of it have been repeated as part of a vast time/ space cosmology.  This
notion is something that is a part of Hinduism, but with a direction towards the
advancement of the spirit.  Nietzsche really honed in on eternal return in his work. 
From an intellectual standpoint, he argued that eternal return means that all ideas are
borne out of something else.  There can really not be something as a "pure" thought or
something that has not come from something else.  In the idea of consciousness, the
challenge is understanding that we, as human beings, are part of a cyclical pattern of
life of being in the world and part of this is repeating.  Eternal return is a concept
that Nietzsche feels adds weight to our existence, pinning us down and making us
recognize an "unbearable burden."  If you are interested in a literary exploration of
this, consider Kundera's The Unbearable Lightness of
Being.