Catholicgauze provides a fantastic diagram showing the difference and similarities between locations within the British Isles, such as England, Wales, Scotland, Northern Ireland, the Republic of Ireland, and Great Britain. I have a short description of these various locales but the diagram is worth a thousand words. Don't forget that Scotland and England are not independent countries.

Comments
Additional to the comments on the site:
Cameroon is also an ‘extra’ member of the Commonwealth, although a small part of the present country did used to be British.
Northern Ireland is not a ‘country’ but a Province.
Surreyman,
Ulster is a province while Northern Ireland is a country. From the offical PM of UK’s website
When did Scotland become a part of the United Kingdom? You have a very informative site.
Sonja L. Marshall
A beginners guide to UK geography from the UK government:
http://www.statistics.gov.uk/geography/uk_countries.asp
England, Scotland, Wales and Northern Ireland are the four countries that make up the UK (the state). (Note that Matt Rosenberg is wrong here).
Whilst these are not independent states, they are different countries.
Scotland became part of the Union in 1707 with the Act of Union – note that they already had the same monarch before this.
Matt Rosenberg has taken a rather simplistic view of the political history of the UK and is promoting a misleading viewpoint based on his self-definition of country and equating country with state.