There seem to be several good places to go that, to me, seem to be
authoritative and readable.
Michael Greene has a page at Cornell University where he paints the broad
outline of what string theory is about and what problems people are working
on. He should know. He and John Schwartz were the co-discoverers of string
theory back in the early 1980's. A slightly more readable account is provided
by
Sunil Mukhi
at the Tata Institute in Bombay, India. A more difficult essay is the one by
Phil Gibbs which goes into many details of how the theory is set up and what
it hopes to accomplish. None of these essays require any mathematics, but as
you will discover for yourself, that does not guarantee that the uninitiate
who knows little or no physics and math, will really understand what this
theory is about in any deep way.