The term shorts referring to garments appears to be derived from the term short pants dating from the 1800s.
The use of the term in the plural appears to follow the usage of pants. While the word pant can be singular, it is most commonly found in the plural.
The word pants itself is derived from pantaloons, which is also most commonly found in plural form. The word pantaloons to signify a type of trousers is derived from a character in sixteenth century Italian Comedia dell' arte, the archetype of which was named Pantalone or Pantaleone who wore long, baggy trousers. How this came to be used in the plural seems obscure.
As a plural noun, shorts does not take a singlular article, such as a. It can be used with the, which can refer to singular or plural nouns. You can say
I want to buy the shorts (a particular pair)
I want to buy shorts (in general)
I want to buy some shorts (which may be one or more pair), or
I want to buy a pair of shorts