Aircraft Systems: Hydraulics, engines, fuel system, avionics, radar, electrical systems, flight controls, structures, etc. i.e. how the airplane mechanically works.
Navigation: How to get from point A to B, calculate winds in flight, calculate fuel remaining, timing, instrument use (TACAN, VOR, ADF, GPS), terrain correlation, etc.
Flight Rules and Regulations: Flying is governed by rules just like driving and you have to know airspace types and restrictions, aircraft separation requirements, speed limits, proper altitudes, fuel reserve requirements, etc.  and a ton more!
Emergency Procedures: If something goes wrong with your aircraft, you have to instinctively react with the correct procedures to save the airplane and yourself.  If the engine catches fire, what do you?
Aerospace Physiology: How does lack of oxygen affect you at altitude?  What do "G"-forces do and how do you counteract them?  How do you guard against fatigue on those 36 hour Global Power missions?  Flying obviously places unique demands on the body that our evolution didn't prepare us for and you must know how to deal with these.  That's one thing that flying computer flight simulators can't capture, how physical it is being in a high performance aircraft.
Maps and Charts: Obviously very important to a navigator.  You have be knowledgeable of map types and scales, magnetic deviation, symbols, where to get them, etc. Lucky for me I majored in Geography at university!
Communications: Talking on the radio is more of an acquired skill than you would think.  Knowing about radio performance, proper terminology, etc. allows you be able to say the right thing when you're supposed to.
Safety: Aviation is inherently risky and you must know the safety aspects of flight to come home in one piece.  Most of our safety of flight procedures and regulations are written in blood.
Aircraft capabilities and performance: To paraphrase Sun Tzu, know oneself to be successful in battle.  This also plays in to safety.
Threat Systems and Tactics: We're not here to be a flying club and thus we must accomplish a mission.  Assuredly there are people who confront us and to defeat them we must possess extensive knowledge of the capabilities of their aircraft, anti-aircraft guns, surface-to-air missiles (SAMs), electronic warfare equipment, etc. and how they intend to employ it.
Tactics: In the face of those threats and to accomplish our mission, we learn procedures or tactics to allow the best chance of success.  This is quite an extensive collection of things to learn and it is constantly changing and evolving.
Counter-tactics: Tactics allow us to accomplish our mission while counter-tactics defeat the enemy's ability to do theirs.  Goes hand-in-hand with threat study.
Electronic Warfare: Kind of an amalgamation of threats, tactics, systems etc.  where we learn threats and how to electronically defeat them and prevent them from doing the same to us.  In the B-1 community, we have to attend a four-month school on this subject alone.
SERE: Survival, Evasion, Resistance, and Escape now known in the field as Evasion and Recovery.  If we get shot down we have to be able to find shelter, food, water, perform first aid, and evade capture.  If we are captured, we must resist the enemy's attempts to exploit us for intelligence and propaganda and hopefully escape to fight another day.  Return with honor is the objective.  We have to attend the dreaded course at Fairchild AFB to learn these skills.  Hopefully, our mastery of threats, tactics, EW, etc. will keep us safe but the enemy gets lucky sometimes.
Weapons: Our mission, to put it bluntly, is to kill people and break things.  Successfully using bombs, fuzes, employment parameters, etc. should allow us to get the job done the first time.  Nobody wants to have to go back to a target twice...
Miscellaneous: In addition to all of these other things, to do our day-to-day jobs we have know about scheduling (puzzle solving) and a ton of other paperwork. Nobody likes it but nothing gets done without it.

A lot of stuff, huh?  In the course of a mission, one will use all of these things and they are all intertwined.  Neglecting anyone of these things can get you killed or cause your mission to fail.  Now you can see why it takes so long to produce a mission ready aircrew.  Furthermore, the learning never stops.  Flying is a perishable skill and you have to constantly study to maintain your edge.  This kind of challenge is immensely rewarding if you can master it.  Push it up!