Whenever you send an email message from Mac Mail, it will reach whatever recipients whose email address was typed into one of the three destination fields: To, Cc (Carbon Copy), or Bcc (Blind Carbon Copy). But Apple Mail also allows you to automatically include yourself in emails you send from it, either as a carbon-copied or blind-carbon-copied recipient - the obvious advantage of that approach is that, unlike relying on the Sent folder to see if you did reply to an email or sent a message, or what you sent to whom, storing your own emails in the mailbox where the responses and other messages of that conversation thread are, gives you a two-sided overview of the discussion, even if it implies storing more data than you strictly need to - we have used this system for years, and are able to find an message long after it was sent, even if the email recipient never replied to it!
(If you do let Mac Mail automatically save a copy of your messages in the Sent folder, it should ideally be purged on a regular basis - which means that a record unanswered emails you sent are gone for good - you would normally rely on a response to see the content of the email you sent yourself, if that makes sense.)
Here's how you can force Mac Mail to include you as automatic email recipient:


You can of course disable and turn off this setting at any point, by following the same steps outlined above, and simply unchecking the "Automatically Cc / Bcc myself" checkbox.