〜させていただく・させてくださる

Verb (causative て-form) + いただくVerb (causative て-form) + くださる

to be allowed to do ~ (humble); someone kindly lets one do ~

About this pattern

Explanation

Very polite way to frame one's own action as permitted: 説明させていただきます = allow me to explain; 休ませてくださいました = (they) kindly let me rest.