If you are using IMAP email then it's probably for the convenience of deleting email from your iPhone and then also having it deleted on your Mac. Same process for sending an email on your iPhone and having it appear in the sent items on your Mac. However more often than not this doesn't work out of the box.
Why it may not be syncing from one device to the other
The key here is that the Sent folder (sent) and Trash folder (deleted messages) must map to the trash and sent folder on your IMAP email 'ON THE SERVER'.
For iPhone / iPad etc
- Mail, Contacts, Calendars
- Select your account e.g. email@example.com
- Click the 'Account'
- Go through each folder 'Sent Mailbox', 'Deleted Mailbox' (Drafts mailbox and Archive Mailbox if you wish) and in each case school down to the corresponding folder 'ON THE SERVER'
- Go back and click 'Done' when you are finished
Your Mac will generally map the sent folder correctly, however interestingly this isn't necessarily;y the case for the 'Deleted Mailbox' and as a consequence if you delete an email from your iPhone it can still show on your Mac - that's a pain.
- In Mac Mail click on your Trash folder on the server. My IMAP trash folder is called 'deleted messages'
- Click 'Mailbox' in the menu
- Use This Mailbox As > Trash Mailbox (or 'Sent)
- You will now see the same deleted /sent items as on your iPhone / iPad
For some reason Mac mail doesn't effectively sync these items in the main Trash folder. I presume this is a Apple Mail bug.