What does the "$" sign mean in jQuery or JavaScript?

In JavaScript it has no special significance (no more than a or Q anyway). It is just an uninformative variable name.

In jQuery the variable is assigned a copy of the jQuery function. This function is heavily overloaded and means half a dozen different things depending on what arguments it is passed. In this particular example you are passing it a string that contains a selector, so the function means "Create a jQuery object containing the element with the id Text".

The $ is just a function. It is actually an alias for the function called jQuery, so your code can be written like this with the exact same results:

jQuery('#Text').click(function () {
  jQuery('#Text').css('color', 'red');
});