verb
To countersign is to sign a document that someone else has signed already.
When you sign a contract for a loan after the borrower has already signed it, this is an example of a time when you countersign the contract.

countersign

a signature added to a document previously signed by another, for authentication or confirmation
a secret sign or signal in answer to another, as in a secret society
MIL. a secret word or signal which must be given to a guard or sentry by someone wishing to pass; password
to authenticate (a previously signed document) by adding one's own signature
countersign

transitive verb
coun·ter·signed, coun·ter·sign·ing, coun·ter·signs
To sign (a previously signed document) to vouch for the authenticity of the document.
noun
A second or confirming signature on a previously signed document. Also called countersignature.
a. A sign or signal to be given to a sentry in order to obtain passage; a password.
b. A secret sign or signal given in answer to another.
countersign

Noun
(plural countersigns)

a second signature added to a document to affirm the validity of the signature of the first person
The response to a sign or signal.
Only those who give the countersign may enter the Masonic Lodge.
Verb
(third-person singular simple present countersigns, present participle countersigning, simple past and past participle countersigned)

To sign on the opposite side of (an instrument or writing).
(by extension) to add a second signature to a document, affirming the validity of the signature of another person
Origin
From Middle French contresigne

countersign - Legal Definition

v

To sign one’s own name next to one’s own or someone else’s to authenticate, reinforce, or verify the first signature.

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