Sensing state of an electrical appliance
Yes.  A current transformer properly applied, preferably to measure the differential mode current thru your device, would be the primary component.  That produces a low voltage and isolated signal proportional to the current drawn by the device.  You then threshold detect that signal, and use the result to drive something that turns a LED on or off.

The details of how to do this are beyond a reasonable answer here for someone that "knows nothing about electrical engineering".  This is like trying to explain in a few written paragraphs how to drive a car, when the explainee has never even seen one.

At your level, you should just go out and get some off the shelf device that does what you want.