What does question mark and dot operator ?. mean in C# 6.0?

It's the null conditional operator. It basically means:

"Evaluate the first operand; if that's null, stop, with a result of null. Otherwise, evaluate the second operand (as a member access of the first operand)."

In your example, the point is that if a is null, then a?.PropertyOfA will evaluate to null rather than throwing an exception - it will then compare that null reference with foo (using string's == overload), find they're not equal and execution will go into the body of the if statement.

In other words, it's like this:

string bar = (a == null ? null : a.PropertyOfA);
if (bar != foo)
{
    ...
}

... except that a is only evaluated once.

Note that this can change the type of the expression, too. For example, consider FileInfo.Length. That's a property of type long, but if you use it with the null conditional operator, you end up with an expression of type long?:

FileInfo fi = ...; // fi could be null
long? length = fi?.Length; // If fi is null, length will be null

It can be very useful when flattening a hierarchy and/or mapping objects. Instead of:

if (Model.Model2 == null
  || Model.Model2.Model3 == null
  || Model.Model2.Model3.Model4 == null
  || Model.Model2.Model3.Model4.Name == null)
{
  mapped.Name = "N/A"
}
else
{
  mapped.Name = Model.Model2.Model3.Model4.Name;
}

It can be written like (same logic as above)

mapped.Name = Model.Model2?.Model3?.Model4?.Name ?? "N/A";

DotNetFiddle.Net Working Example.

(the ?? or null-coalescing operator is different than the ? or null conditional operator).

It can also be used out side of assignment operators with Action. Instead of

Action<TValue> myAction = null;

if (myAction != null)
{
  myAction(TValue);
}

It can be simplified to:

myAction?.Invoke(TValue);

DotNetFiddle Example:

using System;

public class Program
{
  public static void Main()
  {
    Action<string> consoleWrite = null;

    consoleWrite?.Invoke("Test 1");

    consoleWrite = (s) => Console.WriteLine(s);

    consoleWrite?.Invoke("Test 2");
  }
}

Result:

Test 2

This is relatively new to C# which makes it easy for us to call the functions with respect to the null or non-null values in method chaining.

old way to achieve the same thing was:

var functionCaller = this.member;
if (functionCaller!= null)
    functionCaller.someFunction(var someParam);

and now it has been made much easier with just:

member?.someFunction(var someParam);

I strongly recommend this doc page.