Stop setInterval

You need to set the return value of setInterval to a variable within the scope of the click handler, then use clearInterval() like this:

var interval = null;
$(document).on('ready',function(){
    interval = setInterval(updateDiv,3000);
});

function updateDiv(){
    $.ajax({
        url: 'getContent.php',
        success: function(data){
            $('.square').html(data);
        },
        error: function(){
            clearInterval(interval); // stop the interval
            $.playSound('oneday.wav');
            $('.square').html('<span style="color:red">Connection problems</span>');
        }
    });
}

Use a variable and call clearInterval to stop it.

var interval;

$(document).on('ready',function()
  interval = setInterval(updateDiv,3000);
  });

  function updateDiv(){
    $.ajax({
      url: 'getContent.php',
      success: function(data){
        $('.square').html(data);
      },
      error: function(){
        $.playSound('oneday.wav');
        $('.square').html('<span style="color:red">Connection problems</span>');
        // I want to stop it here
        clearInterval(interval);
      }
    });
  }

You have to assign the returned value of the setInterval function to a variable

var interval;
$(document).on('ready',function(){
    interval = setInterval(updateDiv,3000);
});

and then use clearInterval(interval) to clear it again.