An aspect within orb is either closing or opening. If the faster planet is still moving toward exactness, the aspect is applying; once it has passed, the aspect is separating. Traditional astrology treats these as different things rather than as two phases of one thing.
An applying aspect is held to promise: the matter is coming, the perfection has not happened yet, the outcome is still in play. A separating aspect describes something already done and now dispersing. In horary practice, where a question is answered from the chart of the moment it was asked, this is the mechanism the judgement runs on, an applying aspect between the significators says yes, a separating one says the matter is past or will not come together. Bonatti and Lilly both build their rules of perfection and prohibition on it, and it carries more weight in their work than the nature of the aspect does.
Modern natal astrology largely dropped the distinction. A square is a square, and whether it is applying or separating rarely changes the delineation. The traditional revival has been pushing back on this since the 1990s and treats the loss as a real one rather than a simplification, on the argument that an aspect which has already perfected is describing something spent.
The complication is retrogradation. A planet turning retrograde can apply to an aspect, separate from it, and apply again, so the same configuration perfects three times. Traditional sources have specific readings for this; modern natal practice mostly does not, which is a further consequence of having stopped tracking the direction of travel.