(1, p.242) has the following geometric characterization of an inflection point $p$ of a curve $\gamma$ lying on a 2-dimensional sphere.
$p\,$ is an inflection point of the curve $\gamma$ if it has the following property:
Near the connected component of the intersection of $\gamma$ with the tangent great circle $C$ that contains $p$, the curve does not lie on one side of $C$.
What is meant by the curve not lying on one side of $C$?
(1): Tabachnikov, Serge. Differential and symplectic topology of knots and curves. No. 190. American Mathematical Soc., 1999.