Multiple encryption is the process of encrypting an already encrypted message one or more times, either using the same or a different algorithm. It is also known as cascade encryption, cascade ciphering, multiple encryption, and superencipherment. Superencryption refers to the outer-level encryption of a multiple encryption.
Some cryptographers, like Matthew Green of Johns Hopkins University, say multiple encryption addresses a problem that mostly doesn't exist:
Modern ciphers rarely get broken... You’re far more likely to get hit by malware or an implementation bug than you are to suffer a catastrophic attack on AES.
— Multiple Encryption, https://blog.cryptographyengineering.com/2012/02/02/multiple-encryption/ (February 2, 2012)
However, from the previous quote an argument for multiple encryption can be made, namely poor implementation. Using two different cryptomodules and keying processes from two different vendors requires both vendors' wares to be compromised for security to fail completely.