Although Great Britain is a country in itself, England, Scotland and Wales are also considered countries despite sharing a single parliament. How does that work?

In order it goes The United Kingdom (or the U.K.) is the country, Great Britain is the island, and England is one of the U.K.'s four administrative regions along with Scotland, Wales and Northern Ireland.

The United Kingdom
The United Kingdom is an independent country off the northwestern coast of Europe. It consists of the entire island of Great Britain and a northern part of the island of Ireland. In fact, the official name of the country is the "United Kingdom of Great Britain and Northern Ireland."

Great Britain
Great Britain is the name of the island northwest of France and east of Ireland. Much of the United Kingdom consists of the island of Great Britain. On the large island of Great Britain, there are three somewhat autonomous regions: England, Wales, and Scotland.

England
England is located in the southern part of the island of Great Britain, which is part of the country of the United Kingdom. The United Kingdom includes the administrative regions of England, Wales, Scotland, and Northern Ireland. Each region varies in its level of autonomy but all are part of the United Kingdom.

https://www.thoughtco.com/united-kingdom-great-britain-and-england-1435711

The UK (United Kingdom of Great Britain and Northern Ireland) is the oldest and best known example of a sovereign country and UN member containing administrative divisions, also known as countries, each with a devolved parliament, a separate national identity and competing separately in sporting competitions and so on.

The UK is made of four political entities, England, Scotland, Wales and Northern Island. Great Britain or GB is often used as an informal shorthand for the whole country, e.g. at the Olympics, but this is strictly the island made of the mainland parts of England, Scotland and Wales (so doesn't include, say the Scottish isles, Anglesey or the Isle of Wight).

Legally, England, Scotland, Wales and Northern Ireland are referred to as constituent countries, Wales is also a Principality (hence the Prince of Wales) and Northern Ireland is also the Province. Laws of England and Wales have been tied by the Laws in Wales Acts of 1535 and 1542.
https://en.wikipedia.org/wiki/Law_of_the_United_Kingdom#Legal_jurisdictions
https://en.wikipedia.org/wiki/England_and_Wales

Note that the Crown Dependencies of Jersey, Guernsey, the Isle of Man and 14 Overseas Territories around the world are under the sovereignty of the British Crown but are not regarded as part of the UK.

Three other sovereign nations which have constituent countries are:
The Kingdom of Denmark, made up of Denmark, the Faroe Islands and Greenland.
The Kingdom of the Netherlands consisting of the Netherlands, Aruba, Curaçao and Sint Maarten.
French Polynesia, designated an "overseas country" of France, although the status of this is in dispute.
https://en.wikipedia.org/wiki/Country_(disambiguation)#Administrative_divisions