Path of Iron has a similar effect to the Captain enchantment, so it's a great tool for initiators to make sure their team can follow up.
The Tenacity granted by this elixir stacks multiplicatively with other sources, including the passive granted by Mercury's Treads. Still, purchasing this elixir gives access to Tenacity while having other boots in an endgame build.
Elixirs are often bought towards the end of long games when builds are all completed and the extra gold continues to accumulate. They can also be bought mid game to give a temporary stat advantage during ganks and teamfights.
Increased size will give bonus auto-attack range by about 20 or 25 units.