I'll raise some issues. Firstly you say
Do you contrast something against something else here? It implies you say there the preceding sentence
If you throw a ball, it will move along a parabola. Initially its vertical speed will be high, then it will slow down, and then speed up again...
wasn't right, but that sentence seems pretty resonable. The problem is that there are many perspectives/frame to describe the world and all are valid. In particularly you then say
In reality, the ball in moving in a straight line at constant velocity
but that's of course just as relative. If that's true, how is the above sentence not true? In curved spacetime, you can't pic a global inertial spacetime, so I'd not refer to right and wrong velocities in the elaborations.
Now in general relativity, and that's what Danus answer is in particular about, you use another language to specify what straightness is, the mathematical language of Riemannian geometry, and the expressive power of the formulas doesn't really fit into two englisch sentences. The
sections of your explanation is problematic. Because, of course, if you already know Riemannian geometry, you read "straight line" as "solution of the Geodesic equation", but the people who you explain relativity to will not. It's a little like if you don't catch sarcasm. While hearing it, you might understand the words perfectly well but when you come back to think about, what has been said doesn't quite add up.
...but the space-time curvature created by the Earth's gravitation...
Do you have a working definition of "Earth's gravitation"? Because to me it's the space-time curvature around it.
...makes it appear as if the ball is moving in a curved line at varying velocity.
Same velocity-problem as above. Keep in mind that there are frames where your left eyeball is rotating around your nose, and there are frames where your nose is rotating around your mouth.