Leo Strauss' actual teachings are complicated, but Wikipedia actually gives a fairly good simple synopsis:
Among other things, Strauss seemed to believe that almost all the great philosophers of history were saying and teaching the same things, but that they had to be very discreet and hide their real messages. Being a philosopher has been very dangerous over the years, as Socrates (among others) learned the hard way. When you question a society's cherished beliefs, you're asking to be squashed! So, philosophers from Plato on down have had to make their arguments surreptitiously. Strauss believed, for example, that Plato made Socrates out to be a supporter of the established order and oput words in Socrates' mouth that made him seem like no threat to the establishment... but all the while, Plato was sneaking in the opinions he REALLY held (sometimes by ascribing those opinions to disreputable or unlikeable characters).
Part of the appeal of Strauss is that he makes his followers in academia feel as if they're the only ones privy to a big secret. ANYONE can read Aristotle or Descartes, but to a Straussian, half the fun of reading Aristotle or Descartes is in thinking "Aha, I see what Descartes was really trying to say- his 'proof' of the existence of God is so weak, that MUST have been deliberate! Descartes was arguing that God DOESN'T exist. His deliberately weak proof was there to assuage the Church, but he left hidden clues to tip off smart gusy like me as to what he really meant."