Well, this is actually a very in depth subject as the pilot/controller glossary is very big, but I'll list most of the common ones used here. If you have any questions that I don't answer, feel free to ask or PM me and I'll answer any you have.
As far as Alpha, Bravo, Charlie, Delta, Echo, Foxtrot, Golf, Hotel,...
That's the international phononic alphabet, If an Aircraft has a registration issued by the FAA like N74DW, then it would be called into Tower or anyother controller as "Seven, Four, Delta, Whiskey." most times after the initial call they will shorten it to just "four, Delta Whiskey." Most places will use the type aircraft plus the call sign. "Pilatius, Seven, Four, Delta, Whiskey." is a Pilatius aircraft with the registration of 74DW.
Now "Heavy" doesn't exactly mean a full load. The use of the word "Heavy" has a much more important role, Who cares If he has a full load of people? (unless it's an emergency.) what we as pilots and controllers care about is how much the "Heavy" Aircraft weighs. See, the more heavy an aircraft gets the more turbulance/Vortices (In generial terms) it causes in it's wake, a "Heavy" aircraft weighs more then 250,000lbs and requires special handeling when comming in to land or take off. Usually more spacing behind it, because we don't want a smaller aircraft comming in behind it and getting the ever living crap shooken out of it, or worse!
Some others you may hear;
VFR = Visual Flight Rules, pertains to weather and flight regulations.
IFR = Instrument Flight Rules, (see above)
VOR = Very High Omni-Directional Range, a navigation aid
Intersection = A point where 2 or more radials cross from VOR's, or a GPS waypoint used as an intersection.
DME = Distance Measuring Equipment, self-explanitory
ILS = Instrument Landing System
I can go on forever almost, but this should get you started. If you have a specific question as to a specific conversation please feel free to ask it by either PM'ing me or here on the forms. This is only a sample of what is out there as far as things that are said and conversations between pilots and controllers so ask away.
Kevin