Jackets are short, lighter outerwear to keep you warm when the look is casual and the weather not too intense.  The word “jacket” is from the Old French word “jackquette” which is the diminutive of “jaque”.  The name comes from a nickname for French peasants (the first name “Jacques”) and originated from the Arabic “sakk” meaning “coat of mail”. 

Coat of mail:  Flexible armor composed of small overlapping metal rings, loops of chain, or scales.  [Middle English, from Old French maile, from Latin macula, meaning  “mesh”).

So a jacket was the name for a short alternative of the full coat of mail.  It described a coarse and cheap medieval coat of defense, especially one made of leather. 

“Jacket” also applies to the Sport jacket or Sport coat.