On flat paper, two parallel straight lines never meet however far they are extended. That property rests on the paper being flat.
On a sphere, start from two points on the equator and go straight north from each. The two paths set out parallel, yet they always meet at the north pole.
Neither path turns. On a flat surface, going straight and staying parallel go together; on a curved surface they do not.
From high up, drop two objects a little apart at the same moment. As they fall, the gap between them slowly narrows.
Neither object is pushed. Both paths head for the centre of the planet, so the gap changes.
Going straight while the gap changes has the same form as the two paths on the sphere. Even inside a falling box this drawing together cannot be removed. Gravity can be rewritten as the way paths gather, as curvature of spacetime.
Curving space alone cannot explain why things fall to the ground. A thrown ball traces a wide arc in space.
Draw the same motion on a spacetime diagram with on the vertical axis. A flight of seconds becomes km on that axis, and the ball's rise of about m is less than a hundred-millionth of it.
The world line is very nearly straight. What produces its slight bend is that time runs at different rates in different places; the fall of slow objects is set almost entirely by this difference.
Straight, in curved spacetime, is defined by proper time. Among paths joining the same two events, a path with a push along the way means moving faster, and a clock carried along it ticks less.
The clock on the path with no push ticks the most. That path is called a geodesic, and freely falling objects move along geodesics.
Of the two paths in the figure, the clock on the free-fall path advances and the clock on the pushed path (on the figure's scale). The travelling twin's clock falls behind for the same reason.
How much spacetime curves is set by the matter and energy in it. That relation is the Einstein equation.
The left side is the curvature of spacetime, the right side the matter and energy. Matter curves spacetime, and the curved spacetime sets the paths matter follows.
The coefficient is about in SI units. Because it is so small, the curvature made by everyday matter is tiny, and it takes the mass of a star to make it large enough to observe.