I need some explanation of the meaning of sections of the following situation of fiber bundles;
Let $G$ be a topological group such that $G=N\times Z$ where $N$ is normal and $Z$ is central subgroups. Let $H<G$ be a closed subgroup and let $J:=N_G(H^0)$ be the normalizer of the identity component of $H$ then $Z<J$. Now consider the following fibration: $$G/H\to G/J$$ $$gH\mapsto gJ$$ The fiber here is $J/H$. I was reading somewhere the following "since $N$-orbits intersect the fiber $J/H$ in only one point i.e, $eH$, then $N$-orbits are sections of the fibration" Here $N$ is a normal subgroup of $G$.
I don't really understand this. It will be very helpful if you explain it to me. Thanks