IMO mobility. It's what the relative values are based off of, and also what ends the game. No mobility for the king = superior mobility around the enemy king for the side giving checkmate.
So again IMO all other types of advantages (space, structure, initiative, etc) can be derived from the idea of achieving superior mobility of pieces in an area. They are just a means to this end.
Mobility is useless if you don't even know simple tactics, you would just move your pieces around mindlessly.
Tactics are the most important thing but the more mobile you are, the more likely it is that there will be a tactic. Furthermore, tactics are more important at lower levels where most games are won by simple tactics and players constantly trade blunders. If you are <2000, training tactics will help you improve at the greatest rate.
Positional play. As Fischer said, "Tactics flow from a superior position."
Mobility is useless if you don't even know simple tactics, you would just move your pieces around mindlessly.
Tactics are just a manifestation of superior activity.
If he means what is the most fundamental idea in chess, then IMO it's mobility.
If he means what is the most important aspect to study, it's a bad question, you have to take a holistic approach to be good at chess.
If he means what will give a class player the most short term improvement the answer is to study your weakest area / the way you get worse positions in the majority of your games.
For many class players this is tactics, so IMO only in that context can you say tactics.
What is the most important thing in a chess game? Is it the opening, or tactics, or positional play, or pawn structure or piece mobility or what? Please let me know. If you have games illustrating your point, please post them, whether they are your own games, master games or amateur games.