This document is out of date, check the latest tutorial here: http://www.iredmail.org/docs/network.ports.html
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Mail service is complex and required many network service ports, below are network service ports which opened by iRedMail by default:

Ports list:

• Apache (Web server)
  

  • 80: normal web service port

  • 443: HTTPS (http over SSL)

• Postfix
  

  • 25: normal SMTP

  • 587: Submission, SMTP over SSL.

• MySQL
  

  • 3306: default listen port. (Refuse connections from external network in iptables be default)

• OpenLDAP
  

  • 389: normal LDAP port. (Refuse connections from external network in iptables be default)

  • 636: LDAP over SSL. (Refuse connections from external network in iptables be default)

• Dovecot
  

  • 110: POP3 service

  • 995: POP3S (Secure POP3 over SSL)

  • 143: IMAP service

  • 993: IMAPS (Secure IMAP over SSL)

  • 2000: managesieve service. (Refuse connections from external network in iptables be default)

• Policyd (Postfix policy server)
  

  • 10031: default listen port. (Refuse connections from external network in iptables be default)

• Amavisd-new
  

  • 127.0.0.1:10024

  • 127.0.0.1:10025

How to enable network ports you want?

You can edit /etc/sysconfig/iptables (RHEL/CentOS) or /etc/default/iptables (Debian/Ubuntu), add the ports you want to open in it, such as:

#-A INPUT -p tcp -m multiport --dport 80,443,25,465,110,995,143,993,587,465,22 -j ACCEPT
-A INPUT -p tcp -m multiport --dport 80,443,25,465,110,995,143,993,587,465,22,10000 -j ACCEPT

And then restart iptables service to make it work for you:

# /etc/init.d/iptables restart