The email server is a piece of, or a group of software, which transfers emails using SMTP(Simple Mail Transfer Protocol). Email has been there in history of internet for a long time. It has evolved over decades, But the basics still remains the same.
Popular email software in Linux world is Postfix, Sendmail, Qmail, Exim. And in windows one get exchange. Email servers can be as simple as application mail relay. It can be full email suite with IMAP(S), POP3(S), a web client and more.
Email is one of most abused service out there, Most of the breach happens in an organization, the chain starts with email related attack, Phishing attacks are the most successful attack of them all.
There are commercial offering of email services, bundled within a suite and served as SaaS, Popular ones are G-suite, Office-365. These service starts at as cheap is ₹450 per month to ₹1000 per month for a user. When number of user is less than 50, these services makes better sense than to hosting your server. As they take care of the security and administration, They have additional services which increases the productivity and ties you into their ecosystem. Admin have better control over the emails and other services.
Confidentiality of emails should be maintained, Unauthorized person should not be able to view or read the email, Emails should guarantee authenticity that email not modified in its process of reaching the desired recipient.
Few Standards for reference