What is the difference between this:
$.each($(\'#myTable input[name=\"deleteItem[]\"]:checked\').do_something());
and this:
The first will run the callback function to the elements in the collection you've passed in, but your code is not syntactically correct at the moment for it.
It should be:
$.each($('#myTable input[name="deleteItem[]"]:checked'), do_something);
See: http://api.jquery.com/jQuery.each/
The second will run the function on each element of the collection you are running it on.
See: http://api.jquery.com/each/