Vaious D&D 5e sourcebooks mention "metal armor" or "armor made of metal". Here's a few examples:
PHB page 65:
druids will not wear armor or use shields made of metal
PHB page 275:
You have advantage on the attack roll if the target is wearing armor made of metal
Monster Manual, page 262:
If the object touched is either metal armor or a metal shield being worn or carried, its takes a permanent and cumulative -1 penalty to the AC it offers
However, almost any armor has metal elements in it, but few armor is completely made of metal with no other materials. So what is "metal armor"? And what is "armor made of metal"?
For instance, the Studded leather armor is described as
Made from tough but flexible leather, studded leather is reinforced with close-set rivets or spikes.
Providing rivets or spikes are made of metal, does it make the whole armor "made of metal"? Can a druid wear it? Does a Rust Monster do damage to it?
Moreover, even a simple leather armor migh have metal closings/fibulas:
On the other hand, a full-plate gauntlet has non-metal elements (cloth or leather):
Best Answer
This would refer to armor that was primarily metal. As in, you would look at it and say "that armor is made of metal." As opposed to "That is cloth armor" or "that is leather armor." This is supported by a quotation from the Sage Advice column, where it is talking directly about the Druidic Taboo against wearing metal armor.
http://dnd.wizards.com/articles/features/rules-answers-march-2016
Here, we can see that the metal fittings that would normally be added to studded leather do not count as 'Metal Armor.' And, strictly speaking, you can make Leather Armor with fittings other than metal rivets. I am actually a hobbyist Leatherworker and I do know how to make armor. Ideally, you use metal rivets to hold the pieces together...but it's entirely possible to use stitching, bone, or other hard materials in place of the metal.
For a simple test, just read the description of the armor in the PHB. Every description emphasizes the primary material that the armor is made from. For example...
and
and as a final interesting point...
In short, while most of this will be DM-fiat, and it's quite possible to have Dragonscale Scale Mail or a Breastplate made from the carapace of some insectoid creature...as a general rule of thumb, if the description of the armor in the PHB explicitly mentions metal, then you can likely assume that piece of armor counts as 'metal' for the purposes of Druids, Spells, etc.