For a single-founder startup supporting customers via regular email is... OK. Once your business grows - along with your team and the volume of support - you might want to move to a "shared inbox". But a shared mailbox, which is essentially many people being logged into the same mail account, is still missing many features:
You can't check previous communication history with the customer or anyone else from the same company
You can't see if anyone else is currently dealing with the issue or even pass the message between team members
You can't track your team's performance. Even if it's just you and your co-founder - you still want to know your average "first response speed", average "time spent", number of tickets per issue etc.
What's an email ticketing system?
Email ticketing system is a software app that pulls incoming emails from your support mailbox and converts them to tickets for further management and processing in a central database. It automatically distinguishes new tickets from replies to existing ones, and passes along all the file attachments, images, CC-ed users etc.
From the user's perspective it looks like they're just writing you an email - and getting responses. From the support team's side it's an organized database of support tickets that allows them to:
Categorize and tag incoming tickets
Assign tickets to agents
Track time spent on each ticket
Stay within SLA
Look for canned responses or find answers in the knowledge base - internal or publicly available
Prevent agent "collisions" - so two people don't grab the same request simultaneously
Show "who's handling what" - in real time. Like "John is looking at this ticket" or "Caren is already typing a reply"
Automatically suggest articles from the knowledge base to agents, so they can insert it right into their reply
Automate ticket management - via a built-in "if/then" engine
Optionally pull more info about the customer from an external CRM or even integrate with 3rd party software like bug trackers, survey systems etc. Received a bug report? Turn it into a GitHUb issue with literally one click.
Connecting to email server
Most ticketing systems connect to your existing mailboxes via POP3, IMAP or sometimes EWS (Exchange Web Services), pulls the fresh emails, creates tickets (or replies to existing tickets) and then mark the message as "deleted" (or "read") in the mailbox. The message is being pulled with all the file-attachments and inline images. Most systems additionally perform basic spam-checks and antivirus scans.
Once a support agent responds to a ticket - the response is simply being sent back to the user via SMTP.