最近看邮件，发现有人给我回 well received with thanks!
Question : When receive an email from someone, we usually reply that "Well received" or "Well noted". What is it mean? I can not understand clearly of their meaning, just follow to reply.
These two phrases are not being used very well. Well received is used only in the case of a speech or piece of work like an abstract / thesis etc. that is being accepted which is to say that people are agreeing / finding interesting or valid its contents. Certainly would not use this phrase to say that I have gotten someone's email. Well noted just means you have read something and acknowledged it fully and is again not something to use to say that you got an email.
I don't see the need to reply at all. I would not use these phrases at all in this context and would just reply normally without sending unnecessary mail.
( If for some reason required say: "hello, I am just responding to say I have gotten your email and am reading it presently. I will send my response at X time" that would be somewhat okay and not totally bonkers to me.)