I am studying the book "Riemannian Manifolds: An Introduction to Curvature" by Lee. The following statement is from that book.
Let $S^n$ be the sphere of radius $1.$ The Geodesics of $S^n$ are precisely the great circles with constant speed parametrization.
I want to know what he means by ``constant speed parametrization" ad how to obtain such a parametrization when one is already given with a parametrization.
If $\gamma:I\to R^n$ is a curve, then its derivative $\gamma':I\to R^n$ is the velocity vector and its modulus is the so-called speed. So the parameterization $\gamma$ has constant speed if $|\gamma'(t)|=v$ for some positive constant $v>0$.
Any regular curve can be reparameterized to have unit speed. It does not make sense to write down the details here as this is something that you can find in the first chapter of every book on classical differential geometry. For example, in Do Carmo book.