What does "the subgroups of $G$ form a chain" mean? I am being asked to show that: $G$ is a cyclic $p$-group $\iff$ its subgroups form a chain.
What does "its subgroups form a chain" mean? 
Please keep in mind that I am just asking for the meaning of that phrase.

It means that the subgroups of $G$ can be ordered linearly with respect to inclusion:
$$1=H_1 \subseteq H_2 \subseteq \cdots \subseteq H_n = G$$
