I have come across the following Proposition from Milne:
Let $G$ be an affine algebraic group over a field $k$ and $S$ a closed subgroup of $G(k)$. There is a unique algebraic subgroup $H$ of $G$ such that $S=H(k)$ and $H$ ist geometrically reduced. The algebraic subgroups $H$ of $G$ that arise in this way are exactly those for which $H(k)$ is schematically dense in $H$.
So I am wondering what this means for subgroups of $\text{GL}_n(\mathbb{F}_p)$. I have read, that in the setting of finite linear groups, this Zariski-closure is always trivial. What does that precisely mean?
Thanks in advance for explanations.