In brief: An applying aspect is moving toward its exact angle; a separating aspect is moving away after exactness.
Position is not enough
An aspect table usually prints the current angle and its orb. That snapshot alone does not tell whether the pair is approaching or leaving exactness, because planets can move at different apparent speeds and can turn retrograde. Application requires comparison across time: will the absolute deviation from the target angle shrink before either body changes its motion? A separating aspect has already crossed exactness and is widening at that moment.
A simple numerical example
Suppose a slower body is at 12° of a sign and a faster body at 9° of the same sign. If the faster body continues forward, their conjunction gap falls from 3° toward zero, so the aspect is applying. If the faster body has just passed 12° and sits at 14°, the 2° gap is separating. In a real chart, one must use the bodies’ actual dated motion, not assume every named planet is currently direct or always faster.
Astrological use
Traditional and horary approaches commonly give an applying aspect greater weight for a developing matter. Natal and psychological approaches may read both phases with a different emphasis. These are choices of interpretive method, not astronomical outcomes. A transit may approach an exact aspect, separate, then return to it during a retrograde loop. In that case label each pass and its timestamp instead of calling the whole period simply applying.
What confirms the motion
An ephemeris or calculator can show successive dates and exact aspect times. The zodiac and coordinate convention, target angle, allowed orb, and timestamp determine the displayed result. A chart without a dependable birth time may still give planetary longitudes, but Moon contacts near a boundary require a range rather than a single assumed position. “Applying” describes demonstrated motion around the stated instant rather than a visual guess from a static wheel.