একটি গোলকের উপরে বা নিচে লম্ব

When you're flying, what does it mean to be "distance $x$ above the ground" or "at an altitude of $x$"?

Well first, say the Earth is approximately a sphere of radius $r$, with center $O$. Then if you're at a point $P$ in space, that means you're distance $OP$ away from the center of the sphere, so you're distance $PA = OP - OA = OP - r$ above the ground, where $A$ is the closest point to $P$ on "Earth" (the sphere).