There are some spells and perks that require not having armor on to work, so how is armor defined?
Is it just any equippable gear that has additional AC? Is it anything more durable than regular fabric (like leather)?
Mechanically speaking, if I start wearing something that boosts my AC, like a single gauntlet, would that end Stone's Durability, Mage Armor, or Unarmored Defense?
Armor is always referred to in sets. Taking the general description of Heavy Armor from the PHB (pg. 145):
Of all the armor categories, heavy armor offers the best protection. These suits of armor cover the entire body and are designed to stop a wide range of attacks.
Also Plate armor specifically, as an example, from the PHB (pg. 145):
Plate. Plate consists of shaped, interlocking metal plates to cover the entire body. A suit of plate includes gauntlets, heavy leather boots, a visored helmet, and thick layers of padding underneath the armor.
Finally, from PHB (pg. 146), the section on Getting Into and Out of Armor says this for donning armor:
Don. This is the time it takes to put on armor. You benefit from the armor's AC only if you take the full time to don the suit of armor.
From this, it appears to me as though armor is supposed to be worn as a suit, and wearing a single gauntlet wouldn't affect your AC at all.
Therefore, no, wearing a gauntlet won't end the Mage Armor spell or interfere with Unarmored Defense or anything like that, since it doesn't affect your AC.
As an aside, some playable races (such as Lizardfolk from Volo's Guide to Monsters) have "natural armor", and according to this answer to a question about natural armor and Unarmored Defense, natural armor isn't compatible with Unarmored Defense, Mage Armor, etc. as it calculates AC differently.
