an early press that still counts
Input buffering remembers a button press for a short window, usually about 0.1 s, and performs the action on the first frame it becomes possible. Players often press jump a few frames before they land, and without a buffer the game drops that press because the character is still in the air. Both characters here press jump 0.08 s before landing, and only the one with a 0.1 s buffer jumps on the frame it touches down.
Add a jump input buffer: when the player presses jump, set a buffer timer to 0.1 s that counts down every frame, fire the jump on the first frame the player is grounded while that timer is above 0, and reset the timer to 0 when the jump fires so one press gives one jump.