I'm sending an HTML email from APEX and want that whenever the email receiver reply's to the email it is received in Salesforce and I can fire a Trigger in Salesforce as well on the email recieved.
How can this be achieved?
You need to use APEX Email service. You can use email services to process the contents, headers, and attachments of inbound email. For example, you can create an email service that automatically creates contact records based on contact information in messages.
You can find example here Email Services in Salesforce with simple example