noun
respectful term added to addressee's name in letters
A formal, somewhat old-fashioned epistolary expression placed after the addressee's name to show respect, similar to 様 or 御中 but specifically used in written correspondence.
手紙の宛名に「田中様 机下」と書くことがある。
In letters, one sometimes writes 'To Mr. Tanaka, 机下' after the name.
noun
under the desk
Literal spatial meaning; less common than the epistolary sense and may be encountered in older texts or formal contexts.
書類が机下に落ちている。
The documents have fallen under the desk.
The term 机下 literally means 'under the desk', and its respectful usage likely derives from the idea of placing something beneath the desk of a superior as a humble gesture. The exact historical derivation is uncertain.