What is P-Factor in Propeller Aerodynamics?
If the airflow is parallel to the axis of rotation of a propeller, the resulting thrust force will also be parallel to the axis of rotation and act on the center of the propeller disc.

If, however, the airflow hits the propeller at an angle of less than 90°, the resulting force will tilt towards the flow direction and shift away from the center of the propeller disc in a direction orthogonal to the directional change.

Example: You fly in a single-engined plane, the two-bladed prop is spinning clockwise when seen from the pilot's view and you push the left pedal such that the aircraft flies in a sideslip. If both propeller blades are level, nothing much changes, but if the propeller turns another 90°, both blades will see very different flow conditions (see the sketch below):



For the upper blade, which moves from left to right, the sum of circumferential speed ($\omega\cdot r_{Prop}$, red) and air speed ($v_{\infty}$, blue) is bigger than that of the lower blade (black arrows) and hits the blade at a larger effective angle of attack $\alpha_{eff}$. Thus, the lift force created by the upper blade is much bigger, and as a result it will act at a point on the upper half of the propeller disc.

The same happens when the plane flies at a high angle of attack and high power (ground run of a taildragger, or climb) and the airflow hits the propeller disc slightly from below. Now the thrust force will move to the right and tilt slightly downward. This will cause the aircraft to  turn to the left and must be compensated with right rudder.

This effect is sometimes called p-factor, but this is not a factor in an equation, but something you need to factor in when flying at high angle of attack. Note that the rotational component of the prop wash will cause a similar effect when it hits the rudder at an angle, adding to the leftward tendency of the plane.