A formal expression meaning to already be aware of or have consented to something.
その件は先刻承知しておりますので、ご心配には及びません。
I'm already aware of that matter, so there's no need to worry.
先刻承知だ。今さら説明はいらない。
I'm already aware of it. There's no need to explain it now.
彼の希望は先刻承知しているが、実行は難しい。
I'm already aware of his wish, but it's difficult to carry out.