When does an iron rod become magnetic?
Consider a piece of iron as composed of tiny magnets (atoms with dipole moment due to the spin of the electrons) disposed in "domains" which are volumes where the tiny magnets are aligned. The fact is that these domains are a lot and in them the magnets are aligned BUT in total they "neutralize" magnetically the entire piece of iron (to "naturally" reach a "lowest energy state").
Now imagine placing your piece of iron into a strong external magnetic field. The little magnets, previously trapped into their domains, can now align with the external magnetic field.
When you remove the iron from the strong external magnetic field some of the tiny magnets will rearrange themselves again but in general the piece of iron will stay magnetized (due to the domains that changed their internal orientations and stays in the new configuration).
Hope it helps!