An aspect is the angle between two planets in a chart, measured in degrees around the 360-degree wheel. Certain angles recur often enough, and were noticed early enough in the history of astrology, that they each have a name and a traditional meaning attached to how the two planets involved are considered to interact.
The conjunction is zero degrees, two planets sitting close together in the same part of the sky. It blends the two planets' energies together, for better or worse depending on which two planets are involved. The sextile is sixty degrees, generally read as an easy, opportunity-shaped connection. The square is ninety degrees, read as tension or friction, the angle most associated with real, active conflict between two placements. The trine is one hundred twenty degrees, read as the smoothest, most naturally supportive angle. The opposition is one hundred eighty degrees, two planets directly across the wheel from each other, read as a pull between two poles that need to be balanced rather than resolved.
Aspects are not exact-or-nothing. Each one has an orb, a margin of degrees on either side of the exact angle where it is still considered active, just weaker the further it drifts from exact. A conjunction that is off by half a degree is about as strong as it gets. One that is off by seven degrees is barely there. Different aspects and different planets are traditionally given different orb widths, tighter for the fast personal planets, wider for the sun and moon.
In a natal chart, aspects describe permanent relationships between two of your own placements: a natal Venus square natal Saturn describes a lifelong dynamic between how you love and where you feel restricted, for instance. In a transit, an aspect describes a temporary relationship between a moving planet and something fixed in your natal chart, which is why aspects are the actual mechanism behind daily readings: today's reading is really just a list of which aspects between the current sky and your natal chart are close enough to exact orb to be worth mentioning.
Reading a chart well mostly comes down to reading its aspects well: which placements are talking to each other, at what angle, and how tightly. Two charts with identical planets in identical signs can still feel completely different once you account for how those planets are aspected to everything else around them.
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