The term "United Kingdom" was chosen to reflect the fact that the two kingdoms were being united under a single sovereign, but that they would retain their own distinct identities. England and Scotland each had their own parliaments, laws, and customs, and these were preserved under the terms of the union.
The term "United Kingdom" is also used to refer to the larger political entity that includes England, Scotland, Wales, and Northern Ireland. However, the term "Great Britain" is often used to refer to the same area, excluding Northern Ireland.
The term "United Kingdom of Great Britain and Northern Ireland" is the official name of the country, but it is often shortened to "United Kingdom" or "UK" for convenience.