A 'Symmetric' encryption scheme is one where the same secret key is used for both encryption and decryption.
The need to share a key is the main weakness with this type of scheme, since the key can be intercepted by an eavesdropper. This is called the 'Key Distribution Problem'.
Modern symmetric encryption schemes use long, random keys and complex maths for the encryption. If the key is kept secure, they can be very hard to break.