Pull a pendulum back a little and let it go, or pull it back further and let it go, and — within limits — it takes almost exactly the same amount of time to complete one swing either way. That property, called isochronism, sounds like it shouldn't be true: a wider swing obviously has further to travel. It's true because of a second effect that happens to cancel the first one out almost perfectly.
Two effects, working in opposite directions
A pendulum released from a wider angle does have further to travel to complete its swing — but gravity also pulls it back toward the bottom with more force from a wider angle, because more of gravity's pull acts along the direction of motion rather than being wasted pulling against the string or rod. That extra restoring force means the pendulum also moves faster throughout a wider swing. For small swing angles, these two effects — more distance, but proportionally more speed — very nearly cancel out, so the time for one full swing, the period, stays almost constant regardless of how wide the swing is. This is what mathematicians call simple harmonic motion: motion where the restoring force is proportional to how far something has moved from equilibrium, which is exactly the condition that produces this cancellation.
Why "almost" matters, and why it made a clock possible
The cancellation is only exact in the mathematical limit of an infinitely small swing; in reality, isochronism holds closely enough to be useful for swings up to a few degrees, and the period starts measurably lengthening for wider swings. That's precisely why the pendulum clock, refined by Christiaan Huygens in 1656, kept a small, consistent swing rather than a large dramatic one — a small swing meant the clock's timekeeping barely depended on exactly how far the pendulum had been nudged, which mattered because a clock that ran slightly fast or slow depending on how forcefully you set it going would have been useless as a timekeeper. The period of a pendulum's swing instead depends almost entirely on its length and on the strength of gravity, both of which stay constant, which is what let mechanical clocks keep useful time for the first time in history.
What we're still unsure about
The physics of the small-angle pendulum is completely settled and precisely solvable — this isn't a live scientific question. What's harder to predict in any specific real clock is the effect of small real-world disturbances that the idealised model ignores: air resistance, friction at the pivot, and temperature changes that expand or contract the pendulum's length all introduce tiny errors that accumulate over time, and historically much of the engineering ingenuity in precision clockmaking went into compensating for exactly these effects rather than the core physics, which had been understood for centuries.
This sits inside Simple Harmonic Motion, one of eight topics in Mechanics, one of five domains in Physics, one of seventeen subjects the app can quiz you on.