Fencing is like a game of "Rock, Paper, Scissors". Every action a fencer makes can be countered by their opponent. The challenge in fencing is to recognize what your opponent is doing and then to execute the appropriate counter-move. The Tactical Wheel is a convenient way to remember those actions.
In the game of "Rock, Paper, Scissors", each symbol "thrown" beats or is beaten by one of the others; rock beats scissors, paper beats rock, scissors beats paper. The tactical wheel in fencing is similar; parry riposte beats a direct attack, compound attack beats parry riposte, counter attack beats compound attack, and direct attack beats a counter attack.