Armor

Armor (also spelled Armour) is a protective layer of material used to protect something from damage. Some types of armor includes armor for buildings, armor for vehicles and armor for personnel (generally referred to as body armor). This will focus mostly on body armor.

Types of Body Armor

Numerous forms of body armor have been developed over the millennia by civilizations with various levels of technology and resources on hand.

Leather armor - not just any leather would do; soft leather offers no protection against blades. You need hard, boiled leather to be effective. It's a matter of heated debates whether it actually even existed historically, as it's highly impractical and too expensive compared to padded cloth while offering largely the same or even lower level of protection. The general consensus is that it surely didn't have any noticeable presence in Europe, and while in the East (both middle and far) it did exist, it wasn't that much popular and widespread either.
Padded cloth armor - Cloth bundled in sufficient thickness was one of the first forms of armor, since bronze armors tended to be too expensive or too heavy to be widely used, and bronze weapons weren't all that great at cutting to begin with. Cloth continued to be used mostly as padding underneath metal armor, to help absorb blows and all through the middle ages continued to be the go to protection for men-at-arms in lieu of expensive metal plate or mail. Despite what you might think it was quite effective, even against arrows and blades that weren't razor-sharp (and no one sane ever sharpened anything bigger than dagger to razor sharpness), and when things came to crushing blows it was actually the only armor that offered any protection at all.
Paper armor - this one sounds crazy, but apparently it was actually a thing in ancient China. The Mythbusters tested it out and it might have been actually effective... at least, so long as it doesn't rain.
Scale armor - an early form of mail, using overlapping metal plates rather than rings. The scales would overlap in a similar fashion to roofing tiles.
Bamboo armor - basically wooden armor, but with the advantage in that you can shape bamboo more easily.
Mirror armor - an early form of plate, this was a small round bronze plate attached to the torso. Besides physical protection, it was also believed to ward off the supernatural.
Mail - the most common and effective type of armor from the ancient world to the middle ages. Flexible and easy (though time-consuming) to make, it was widely used by many cultures. It was also significantly easier to repair, as a break could easily be mended by replacing a few rings, whereas a hole in plate armor might require a complete replacement. While fairly effective against foot soldiers, the crossbow and the lance charge required knights to wear extra armor over mail for additional protection.
Plated Mail - this is not what some sourcebooks refer to as platemail, which is basically just plate armor worn over a mail hauberk. Plated mail integrates metal plates into the rest of the mail pattern, ranging from large rectangular plates on areas like the chest, to small plates arranged like fish scales on areas that require more dexterity, such as near the shoulders and back. This was popular with medieval Persians and Indians.
Laminar armor - armor made from bands of metal. The most famous example is the ancient Roman Lorica Segmentata.
Lamellar armor - armor made from overlapping pieces of leather or metal, each piece being laced side-by-side.
Samurai armor - depending on the period, it could be lamellar, laminar, or even plate. The helmet (kabuto) had a distinct shape that often featured ornaments and even a removable facemask (Darth Vader's helmet is said to be a hybrid of a kabuto and a German stahlhelm).
Brigandine - Sort of like Lamellar, except the pieces of metal are riveted into a leather jacket rather than laced together.
Plate armor - armor made from single, solid pieces of metal. Bronze plate armor had been used in ancient times, but was limited to helmets and sometimes breastplates due to the weight of the armor. Full suits of plate armor were not possible until improvements in smithing allowed for large bars of steel to be hammered out into single pieces.
Flak Jackets - The first modern armor to be developed, Flak Jackets were developed in WWII out of high-strength nylon to protect aircrews from fragments fired from flak cannons. Before the invention of Kevlar and ballistic vests, this was the only kind of armor available to modern soldiers.
Ceramic armor - typically, ceramic plates are used as an energy-absorbing component in some ballistic vests. These are typically single-use only.
Ballistic vests - cloth vests able to stop bullets of varying sizes using high-strength cloth that wraps itself around the bullet, thereby bringing them to a halt. May contain metal or ceramic components to increase effectiveness.
Blast suits - full-body armors capable of absorbing the heat and shrapnel of a bomb blast. The only part that isn't protected are the hands, so if a bomb goes off you may be maimed - but at least you're not dead! May also include a closed air supply in the case of biological or chemical bombs. Commonly worn by EOD technicians.

Anatomy of armor

You thought we were joking about the dick armor?

Basic terminology of the different parts of armor. Unless you were very wealthy, such as a knight, not everyone had every part of their body covered in armor.

Helmet - protects the head, one of the most common pieces of armor.
Gambeson - padded cloth armor suit worn underneath metal armor to absorb blunt force and protect the wearer from the armor itself (metal and boiled leather aren't nice to unprotected humans skin, especially under extreme temperatures). Later variants often reinforced with sown-in mail in places actual metal armor above it have gaps and joints.
Cuirass - protects the torso. If its made from a single piece of metal, it is a breastplate. Most breastplate are associated with full-body steel plate armor, but ancient Greeks had a bronze version called the "heroic Cuirass", or the Roman "Lorica Musculata", often molded with fake muscles and various decorations.

Plackart - lower torso reinforcement that would overlap with a breastplate for extra protection, and connected to the faulds.
Faulds - a metal skirt attached to the breastplate, allowing some leg protection while offering mobility.

Gorget - protects the neck. With certain helmets, such as the Sallet, the gorget protected the lower head where the helmet did not.
Pauldrons - protect the shoulders. The real life versions are nowhere near as big as those on space marines.
Gauntlets - protect the arms.
Greaves - protect the legs.
Sabatons - protect the feet (you don't want some smartass spearman stabbing at your unarmored feet now, would you?)
Codpiece - Yes, believe it or not, you could get dick armor too. Ordinarily this was just to armor the groin area like an athletic cup, but some people like King Henry VIII made massive codpieces to show off how well-endowed they were.
Tabard - Technically not armor, but was the decorative sleeveless coat that would drape over the armor of knights. Besides being used as an identifier through the knight's heraldry, it also shielded armor from the desert sun so that the knight wouldn't boil in their own armor.