What is symmetric key cryptography?

Answer 1

An system in which the sender and receiver share a single, common key that is used to encrypt and decrypt the message. Say you are given a message "Hello World" and Your key is the "K" then

"Hello World" + "K" = Encrypted Message 
Encrypted Message + "K" = "Hello World"  (Assume + as crypto operation)

In comparison to public-key algos, which utilizes two keys - a public key to encrypt messages and a private key to decrypt them.

Symmetric-key systems are simpler and faster, but their main drawback is that the two parties must somehow exchange the key in a secure way which is not the issue with Public Key encryption as only public key is shared and private key is never shared.

Answer 2

An encryption system in which the sender and receiver of a message share a single, common key that is used to encrypt and decrypt the message. Contrast this with public key-cryptology, which utilizes two keys - a public key to encrypt messages and a private key to decrypt them. Symmetric-key systems are simpler and faster, but their main drawback is that the two parties must somehow exchange the key in a secure way. Public-key encryption avoids this problem because the public key can be distributed in a non-secure way, and the private key is never transmitted. Symmetric-key cryptography is sometimes called secret-key cryptography. The most popular symmetric-key system is the Data Encryption Standard (DES).

Ref: http://www.webopedia.com/TERM/S/symmetric_key_cryptography.html