Get clicked element using jQuery on event?

As simple as it can be

Use $(this) here too

$(document).on("click",".appDetails", function () {
   var clickedBtnID = $(this).attr('id'); // or var clickedBtnID = this.id
   alert('you clicked on button #' + clickedBtnID);
});

The conventional way of handling this doesn't play well with ES6. You can do this instead:

$('.delete').on('click', event => {
  const clickedElement = $(event.target);

  this.delete(clickedElement.data('id'));
});

Note that the event target will be the clicked element, which may not be the element you want (it could be a child that received the event). To get the actual element:

$('.delete').on('click', event => {
  const clickedElement = $(event.target);
  const targetElement = clickedElement.closest('.delete');

  this.delete(targetElement.data('id'));
});

You are missing the event parameter on your function.

$(document).on("click",".appDetails", function (event) {
    alert(event.target.id);
});