Equivocation is a situation when a cryptanalyst trying to extract the plaintext from the ciphertext, discovers more than one plausible plaintext that could have encrypted to the very same ciphertext.
If all the plausible plaintexts are of equal likelihood then the cryptanalyst finds himself at an impasse of equivocation.
The set of plausible messages could together yield some useful information, or not, but it would be impossible cryptographically to narrow down the field.
Unlike eroding intractability  equivocation is durable!
Equivocation may be with two plausible ciphertexts, or with many.
By using a key as large as the message it is mathematically possible to insure an unbreakable cipher (known as the Vernam cipher, or OneTimePad).
By paying with the inconvenience of using the large keys needed for equivocation one buys perfect mathematical security for his secrets.
May be very helpful and very powerful for communicating highly sensitive small messages, like keys for other ciphers.
In 1917 Gilbert S. Vernam (Bell Labs) has patented a cipher offering absolute equivocation. This may be the most pivotal event in the history of cryptography.
Vernam cipher spawned a wave of cryptographic activity trading the poor convenience, and inherent weaknesses offered by Vernam with a measured loss of equivocation security. 
