The SharePoint Directory Management service connects SharePoint sites to your organization's user directory to provide enhanced e-mail features. The benefit of using this service is that it enables users to create and manage e-mail distribution groups from SharePoint sites. This service also creates contacts in your organization's user directory so people can find e-mail-enabled SharePoint lists in their address books. However, using SharePoint Directory Management service requires more management because it is communicating with Active Directory Domain Services (AD DS).
Check this post to know the detailed purpose of SharePoint Directory Management service.
Check this post for detailed info on how DMS is configured for Incoming emails.