perihelion precession
A planet on a perfect Newtonian orbit around a lone Sun traces the same closed ellipse forever, its point of closest approach, the perihelion, fixed in space. General relativity spoils this perfect closure: the ellipse itself slowly rotates, so the perihelion creeps forward a little with each orbit and the path traces out a slowly turning rosette. For Mercury, the innermost planet, this relativistic creep is small but real, and its explanation was the first triumph of Einstein's theory.
The extra rotation predicted by general relativity, on top of any Newtonian effects, is Delta phi = 6 pi G M / (c^2 a (1 - e^2)) radians per orbit, where a is the semi-major axis and e the eccentricity. For Mercury this works out to about 43 arcseconds per century. It arises because in the Schwarzschild geometry the effective potential governing the orbit has an extra term, going as 1 / r^3, absent from Newton's inverse-square law, and it is that term that stops the orbit from closing.
The importance of this result is historical and decisive: unlike light bending, which was a fresh prediction, the 43 arcseconds per century were a known, unexplained anomaly. Astronomers had measured Mercury's perihelion advancing and, after subtracting every Newtonian nudge from the other planets, were left with a stubborn residual that no one could account for. Einstein's theory produced exactly that number with no free parameters. The honest framing matters: the total observed precession is about 5600 arcseconds per century, the vast majority of it ordinary Newtonian perturbation and the frame's own rotation; general relativity is responsible only for the leftover 43.
Of Mercury's observed roughly 5600 arcseconds per century of perihelion advance, about 5025 come from the precession of Earth's own reference frame and 532 from tugs by the other planets; the final 43 arcseconds, unexplained for decades, are precisely what general relativity supplies.
The famous 43 arcseconds are the small relativistic residual, not the whole precession.
General relativity did not explain all of Mercury's precession, only the anomalous 43 arcseconds per century that Newtonian gravity left over. Presenting the 43 as the total is a common oversimplification; almost everything else is ordinary celestial mechanics.