How can I set a reminder for a specific user to be triggered on a specific date?
Rules module
Use the Rules module together with Rules Scheduler (a sub-module of it), as explained in the 3 steps below. These steps are based on a date field which is added to the user profile, so that for each user you can indicate an appropriate date.
Step 1: Create a field to store the appointment date
Add a field to the &quot;user&quot; entity with machine name (say) field_next_appointment. Allow only 1 date (to store the &quot;next&quot; appointment), but don't make it required.
Step 2: Create a Rules &quot;Component&quot;
Here is the Rules Component to be created (in Rules export format, just import it in your own environment via copy-paste, which you can do using the &quot;Import rule&quot; link located at admin/config/workflow/rules):
{ &quot;rules_send_email_notification&quot; : {
    &quot;LABEL&quot; : &quot;Send eMail notification&quot;,
    &quot;PLUGIN&quot; : &quot;action set&quot;,
    &quot;OWNER&quot; : &quot;rules&quot;,
    &quot;REQUIRES&quot; : [ &quot;rules&quot; ],
    &quot;USES VARIABLES&quot; : { &quot;user_to_notify&quot; : { &quot;label&quot; : &quot;User to be notified&quot;, &quot;type&quot; : &quot;user&quot; } },
    &quot;ACTION SET&quot; : [
      { &quot;mail&quot; : {
          &quot;to&quot; : [ &quot;user-to-notify:mail&quot; ],
          &quot;subject&quot; : &quot;Friendly reminder about your upcoming event&quot;,
          &quot;message&quot; : &quot;This is a reminder about the upcoming event that you have an upcoming event on [user-to-notify:field_next_appointment] ...&quot;,
          &quot;from&quot; : &quot;[site:mail]&quot;,
          &quot;language&quot; : [ &quot;&quot; ]
        }
      }
    ]
  }
}

Obviously, the Subject and Content of the eMail may need review / tuning, while you might also want to use some other From eMail ID.
Step 3: Create a &quot;Rule&quot; using the Rules Component
Here is the Rule to be created, in Rules export format (just import it in your own environment via copy-paste, which you can do using the &quot;Import rule&quot; link located at admin/config/workflow/rules):
{ &quot;rules_on_new_user_event_registration&quot; : {
    &quot;LABEL&quot; : &quot;On new user event registration&quot;,
    &quot;PLUGIN&quot; : &quot;reaction rule&quot;,
    &quot;OWNER&quot; : &quot;rules&quot;,
    &quot;REQUIRES&quot; : [ &quot;rules&quot;, &quot;rules_scheduler&quot; ],
    &quot;ON&quot; : { &quot;user_update&quot; : [] },
    &quot;IF&quot; : [
      { &quot;entity_has_field&quot; : { &quot;entity&quot; : [ &quot;account&quot; ], &quot;field&quot; : &quot;field_next_appointment&quot; } }
    ],
    &quot;DO&quot; : [
      { &quot;schedule_delete&quot; : {
          &quot;component&quot; : &quot;rules_send_email_notification&quot;,
          &quot;task&quot; : &quot;[account:name]&quot;
        }
      },
      { &quot;schedule&quot; : {
          &quot;component&quot; : &quot;rules_send_email_notification&quot;,
          &quot;date&quot; : {
            &quot;select&quot; : &quot;account:field-next-appointment&quot;,
            &quot;date_offset&quot; : { &quot;value&quot; : 259200 }
          },
          &quot;identifier&quot; : &quot;[account:name]&quot;,
          &quot;param_user_to_notify&quot; : [ &quot;account&quot; ]
        }
      }
    ]
  }
}

Note that the above rule refers to the Rules Component from the previous step.
Also note the machine name of field_next_appointment in this rule, which is the field's machine name created in Step 1 (if in step 1 you used another machine name, then also replace the machine name field_next_appointment in this rule with the machine name of the field created in Step 1 (if you don't have such field yet, or the field names don't match, then the import of the above rule might not work).
The schedule_delete that is part of this rule is to ensure that previously &quot;scheduled&quot; reminders will get removed when updating the data field (so that it only triggers 1 reminder, and with the most recent date).
Step 4: Further tuning and enhancements

The date_offset (=259200) in the above rule corresponds to &quot;3 days in advance&quot;, which may need review / tuning.

If needed, you could also use the Field Permissions module to set field-level permissions to edit, view and create fields on any entity.

Instead of just sending an eMail (as in the Rules Component), you could replace that by a more advanced option using the Message module (which has great integrations with the Rules module also). Here is an quote about that module (from its project page):

... enables logging and displaying system events in a number of different use cases. Events that are recorded over time are sometimes call activity streams. Exportable messages subtypes can be created for different use cases with custom fields and display (view) modes.



Note: Using Rules to send an email X days after a user registers also contains quite some details that may help you.
Date Reminder module
There is also the Date Reminder module. Here is a quote about this module (from its project page, bold markup added here):

... allows a registered user to request an email reminder to be sent at a specified time before an event. Generally these would be calendar events, but any node type that has a CCK datetime can support reminders.

However I think that module is not going to answer your question, because:

it's the user who has to request such reminder (in your question you want to set a reminder to a specific user).
these reminders are related to some node, while your question is related to a user. You might possibly work around this by creating some extra node type (like &quot;Appointment&quot;?), though that seems like overhead.