Hi Pries, 

You have to check if description is null or empty at line number 39 and update the value accordingly. Please see below complete code:
 

trigger TaskCompletedTrigger on Task (before update ) {
    Set ownerIds = new Set();
    for(Task tsk: Trigger.New){
        if(tsk.Status=='Completed'    && Trigger.oldMap.get(tsk.Id).Status != 'Completed'){
            ownerIds.add(tsk.CreatedById);
        }
    }
    
    Map userMap = new Map([select Name, Email from User where Id in :ownerIds]);
    Map mapCase = new Map([SELECT Id,CaseNumber,CreatedDate,Status,Description,Type,Subject,Contact.Name,Contact.Email,Contact.MobilePhone  FROM Case]);
    List emailMsglist=new List();
    
    for(Task tsk : Trigger.New) {
        Case caseObj  = mapCase.get( tsk.WhatId );
        if(tsk.Status=='Completed' && Trigger.oldMap.get(tsk.Id).Status != 'Completed'){
            User theUser = userMap.get(tsk.CreatedById);
            Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
            String[] toAddresses = new String[] {theUser.Email};
            mail.setToAddresses(toAddresses);    
            mail.setSubject('A task has been updated');     
            String template = 'Hello {0}, \nYour task has been Completed. Here are the details - \n\n';
            template+= 'CASE- {1}\n';
            template+= 'Subject - {2}\n';
            template+= 'Due Date - {3}\n';
            System.debug('*** Comments *** ');
            template+= 'Comments - {4}\n';
            template+= 'Status - {5}\n';
            String duedate = '';
            String Commentsdes = '';   
            
            if (tsk.Description==null )
                Commentsdes = 'No Comments';
                
            if (tsk.ActivityDate==null) 
                duedate = '';
            else
                duedate = tsk.ActivityDate.format();
            
            Commentsdes = tsk.Description;  
            List args = new List();
            args.add(theUser.Name);
            args.add(mapCase.get(tsk.WhatId).CaseNumber);
            args.add(tsk.Subject);
            args.add(duedate);
            args.add((String.isEmpty(tsk.Description)?'':tsk.Description));
            args.add(tsk.Status);
            
            
            String formattedHtml = String.format(template, args);
            mail.setPlainTextBody(formattedHtml);
            emailMsglist.add(mail);
        
        }      
    }
    Messaging.SendEmail(emailMsglist);

}

Please mark this as best answer if this resolves problem.

Thanks