Any effective cryptographic system that cannot be broken by the best computer technology available today and in the foreseeable future, i.e. any ciphertext that is safe from the prying eyes of the National Security Agency. As of 2001, strong cryptography would mean a block cipher with a key length of 128 bits or more and an RSA or ElGamal modulus of 1024 bits or more. Oppose kid sister encryption.
For a very long time strong cryptography was considered dangerous munitions by the US Government, meaning export of programs that used strong cryptography was restricted by the ITAR rules. If you sold strong crypto to foreign nationals without an export license you would be considered an illegal arms dealer, and be dealt with as though you had sold a nuclear device to a group of terrorists. However there have been recent court rulings (thanks to Dan Bernstein) that served to relax these restrictions, but it seems that the events of September 11, 2001 are going to undo all of that.