A while ago, when I was looking at read-only auto-properties I started comparing them to the previous method of making a property read-only by making it private. When it comes down to it there are a few differences how they can be initialised and read/written to. At the time I put together this example. Comments explain where and how each property can be accessed.

void Main()
{
	Person firstPerson=new Person(new DateTime(2001, 10, 16));
	
	// Unrestricted access to FirstName and LastName
	firstPerson.FirstName="John";
	firstPerson.LastName="Jones";
	
	// Cannot access Date Of Birth, other than via consructor or within class membes internally
	//firstPerson.DateOfBirth= new DateTime(1926, 03, 27);
	//firstPerson.Age = 34;
		
	// Accessing readonly property directly produces a compile time error
	firstPerson.ChangeDateOfBirth(new DateTime(1926, 03, 27));
	
	// Uncomment if runnning with LinqPad
	//Console.WriteLine(firstPerson);;
}

public class Person{

	// Unrestricted access
	public string FirstName{get; set;}	
	public string LastName{get; set;}	
	
	// Accessible only by Constructor
	public DateTime DateOfBirth {get;} // Date
	
	// Accessible by Contructors and internally to the class members
	public int Age {get; private set;}
	
	
	public Person(DateTime dob){
		DateOfBirth = dob;
		
		Age=-1;
		CalculateAge();
	}
			
	public void CalculateAge(){
		// Validat Date set before calculation
	
		// Implementation to calculate the age from the DateOfBirth
		DateTime today = DateTime.Today;
		Age = today.Year - DateOfBirth.Year;
	    if (today.Month < DateOfBirth.Month || (today.Month == DateOfBirth.Month && today.Day < DateOfBirth.Day))
		{
        	Age--;
		}
	}
	
	public void ChangeDateOfBirth(DateTime dateOfBirth){
		// Compile time error when trying to access readonly property
		//DateOfBirth = dateOfBirth;
	}
}

I have made this example available as a Gist here