"Enter key pressed" event-handler
A few things to note before I explain improvements


Never forget var when declaring variables. I saw this in the code.

email = subscriberInput.val();


Now, best case scenario is that you declared email somewhere in the higher scopes. However, if it wasn't then JS will declare it as a global, which may have unforseen negative effects.
If you run a site that has translation capabilities, I suggest you don't hard-code messages. Use translation libraries instead. That way, you can globally change language with just a flick of a switch.


Then here's the improved code, given what you have:

subscriberInput.keyup(function (event) {

  // If you intent to prevent the default action of the enter, then I
  // suggest preventDefault() instead of return false
  event.preventDefault();

  // I recommend the "return if fail" pattern rather than "run when true"
  // because it removes unnecessary indentation. It's a case to case basis.
  if (event.which !== 13) return;

  $.post("/en/subscriber/add", {
    // The context of the function is the input box. We can simply use
    // the value property instead of calling out val()
    email: this.value
  }).done(function (data) {

    // Similar to above, use strict comparison as much as possible
    if (data === "success") {

      // Avoid repeating code by factoring out common code. In this case,
      // what set the code apart was the message.
      var message = isEnglish ? "You're subscribed!" : "Sunteti abonat cu success";

      subscribeBox.find('div.row')
                  .remove();

      // jQuery actually has a delay() function which can delay animations.
      // Better than using timers manually.
      subscribeBox.find('h5')
                  .addClass('green-text')
                  .text(message)
                  .delay(5000)
                  .fadeOut('slow');

    } else {

      // Now I don't know why you are doing the alert. If you are debugging,
      // I suggest you use console.log() or a custom logging library.
      alert(data);
    }
  });

});