The encryption key is simply related to the decryption key, in that they may be identical or there is a simple relation between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private secure connection.
Other terms for symmetric-key encryption are secret-key, single-key, shared-key, one-key and eventually private-key encryption. Make sure that the use of the latter term does conflict with the term private key in public-key cryptography.
Symmetric-key algorithms can be divided into stream ciphers and block ciphers. Stream ciphers encrypt the bits of the message as a stream of bits one at a time, and block ciphers take a number of bits and encrypt them as a single unit. Blocks of 64 bits have been commonly used; though modern ciphers like the Advanced Encryption Standard algorithm uses 128-bit blocks.