filter composed of identical sections
\$Z_{iter}\$ is the impedance of an infinite series of identical filter sections.

If you take one section away from an infinite series, you still have exactly the same infinite series - infinity minus one is still infinity. Therefore, adding or removing any number of sections must not change the impedance.

Start with an impedance of \$Z_{iter}\$ (which represents the infinite series), add another filter section in front of that, and then recognize that the impedance of this overall circuit is still \$Z_{iter}\$. Now the harder part is to actually solve this to find out which value of \$Z_{iter}\$ can be equal to these two impedances at the same time.