1feeling obliged; being grateful or thankful (often used politely to express appreciation).
手伝っていただき、誠に恐縮です。
Thank you very much for your help; I am truly grateful.
ご連絡くださり恐縮です。早速確認いたします。
Thank you for contacting me; I appreciate it. I will check immediately.
皆さんのおかげで合格できて恐縮です。
I'm very grateful to everyone for helping me pass.
2feeling sorry or embarrassed (for troubling someone, being ashamed, or feeling awkward when praised); often used before requests as '恐縮ですが...'.
恐縮ですが、明日の会議を延期していただけますか。
I'm sorry to ask, but could you postpone tomorrow's meeting?
お手数をおかけして恐縮ですが、書類をご確認ください。
Sorry to trouble you, but please check the documents.
褒められて少し恐縮してしまった。
I was a bit embarrassed by the compliment.
3archaic: to shrink back in fear; to cower (rare/old-fashioned meaning).
古い物語では、恐ろしくて民が恐縮する場面が描かれることがある。
In old tales, there are scenes where people cower in fear.