What is the origin of High Street (and Highway)?

The term high comes from the Old English usage meaning main, excellent in type or degree (also high society, high priest have the same connotation) as suggested by the following sources:

High Street

  • We have to go back a very long way to search out its origin. In Old English, the word high meant something excellent of its type or of elevated rank or degree (we still have terms like high society, high priest and high sheriff that are based on it).
  • Very early on, high began to be applied to main roads. The first example is highway, recorded from the early ninth century. This referred to a main road between two towns or cities, one that was under the special protection of the monarch as an essential communications link (hence the later phrase the king’s highway to refer to such important roads).

From World Wide Words

Highway:

  • Old English heahweg "main road from one town to another;" see high (adj.) in sense of "main" + way (n.). High street (Old English heahstræte) was the word before 17c. applied to highways and main roads, whether in the country or town, especially one of the Roman roads.

  • In more recent usage, it generally is the proper name of the street of a town which is built upon a highway and was the principal street of the place. Highway robbery is from 1707; as a trivial expression for something too costly, 1886.

Etymonline