Each electromechanical machine can be basically represented in two axes: direct (excitation) and quadrature (torque) which are perpendicular to each other. The torque is a product of both components, the Q is variable, while the D is constant in the nominal range of operation.
The easiest motor to understand is the permanent magnet DC motor. The D-axis is the permanent magnet - excitation, the rotor field is perpendicular to magnet and it is a Q-axis.
The induction motor follows the same rule, the current in the rotor cage produces a magnetic field that is summed to the rotating stator field, indeed these resultant field can be split into the Q and D components. As the torque is proportional to the product of D and Q components, it is obvious that larger current produces larger torque.