The causative verb in the te-form followed by ください is a polite request for permission for an action performed by the speaker. In other words, the speaker humbly seeks the hearer's permission to do something. ~くださいませんか is more polite than ~ください.
この電話を使わせてください。
Please let me use this telephone.
あしたは休ませてくださいませんか。
Could you please let me take a day off tomorrow?