You have to catch the submit event on the form. If the input is invalid, then prevent the default behavior.
$("form").on("submit", function () {
    var isInvalid = false;
    $("input", this).each(function () {
        if (!$(this).val()) {
            isInvalid = true;
        }
    });
    if (isInvalid) {
        return false;
    }
});
If you only need to catch the blur event then, just do it!
$(document).ready(function() {
  var $error = $(".alert-danger");
  $("form input").on("blur", function() {
    if (!$(this).val()) {
      $error.removeClass("hide").text("No value");
    } else {
      $error.addClass("hide");
    }
  });
});
@import url("https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css");
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div class="container">
  <form action="">
    <input type="text" class="form-control" placeholder="Text input">
    <div class="errors">
      <div class="alert alert-danger hide"></div>
    </div>
  </form>
</div>