This is the 4855th most frequent Spanish word.
den
"Den" in Spanish means "give" (plural command form of "dar").
Here, 'den' is the subjunctive form used as a polite imperative form directed to multiple people, derived from 'dar', which means 'to give'.
Por favor, den las gracias al anfitrión.
Please, give thanks to the host.
'Den' here refers to 'dar' in the subjunctive form for third person plural (ellos/ellas), used to express a wish or hope.
Espero que den lo mejor de sí mismos en los exámenes.
I hope they give their best during the exams.
In this case, 'den' is addressing a group of individuals formally, requesting them to provide their consent.