You use hereby when officially or formally saying what you are doing. [ADV before v] [Formal]
I hereby sentence you for life after all the charges against you have been proven true…
鉴于对你的所有指控都证明属实，我特此宣判你无期徒刑。
You are hereby appointed Sub-lieutenant RNVR of HMS Tartar…
你被任命为皇家海军舰艇“鞑靼人”号的皇家海军志愿后备队中尉。
I am offended that your entertainment expert should make such a mistake and hereby request a formal apology.
令我感到气愤的是，你们的娱乐节目专家竟然会犯这样的错误，我特此要求你们向我正式道歉。