Mum's the word is a popular English

English language

English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

 idiom

Idiom

Idiom is an expression, word, or phrase that has a figurative meaning that is comprehended in regard to a common use of that expression that is separate from the literal meaning or definition of the words of which it is made...

. It is related to an expression used by William Shakespeare

William Shakespeare

William Shakespeare was an English poet and playwright, widely regarded as the greatest writer in the English language and the world's pre-eminent dramatist. He is often called England's national poet and the "Bard of Avon"...

, in Henry VI, Part 2

Henry VI, part 2

Henry VI, Part 2 or The Second Part of Henry the Sixt is a history play by William Shakespeare believed to have been written in 1591, and set during the lifetime of King Henry VI of England...

.

Meaning

"Mum's the word" means to keep quiet, to say nothing. "Mum" is a Middle English

Middle English

Middle English is the stage in the history of the English language during the High and Late Middle Ages, or roughly during the four centuries between the late 11th and the late 15th century....

 word meaning "silent". The word may be derived from the "mmm" sound made when one tries to speak with lips closed.
Note the phonetically similar German word "stumm" (Old High German

Old High German

The term Old High German refers to the earliest stage of the German language and it conventionally covers the period from around 500 to 1050. Coherent written texts do not appear until the second half of the 8th century, and some treat the period before 750 as 'prehistoric' and date the start of...

 "stum", Latin "mutus") meaning "silent, mute".

Origin

The origins of the phrase can be traced back to the fifteenth century Towneley Plays

Wakefield Mystery Plays

The Wakefield or Towneley Mystery Plays are a series of thirty-two mystery plays based on the Bible most likely performed around the Feast of Corpus Christi probably in the town of Wakefield, England during the late Middle Ages until 1576...

and notably in Shakespeare's Henry VI, Part 2

Henry VI, part 2

Henry VI, Part 2 or The Second Part of Henry the Sixt is a history play by William Shakespeare believed to have been written in 1591, and set during the lifetime of King Henry VI of England...

, Act 1, Scene 2: