The Union Flag, which most people call the Union Jack, is the flag that represents the United Kingdom so it is the British flag. It got it's name because it symbolises the union between the UK countries - England, Northern Ireland, Scotland and Wales. The flag incorporates the three flags of England, Northern Ireland and Scotland.
In 1194 AD, Richard I of England introduced the Cross of St George (most commonly known now as St George's Flag) at the national flag of England. It is a red cross on a white ground.
After Queen Elizabeth I died in 1603, it was the Scottish King James VI who took the throne in England and became King James I of England. It was in 1604 that King James declared himself the King of Great Britain and joined both England and Scotland together as one nation. This caused problems for sailors on chips because they didn't know which flag they should have hoisted on the king's ships, English sailors didn't want the Scottish flag and the Scots didn't want the St George's flag.
It was because of this problem that the two flags were merged to form the first Union flag in 1606 and it was 100 years later, on 28th July 1707, that Queen Anne made a royal proclamation that this was made the National flag of Great Britain and it began being used both on land and at sea. Scotland and England were officially one kingdom, with one united monarch and parliament.
Another 100 years later, in 1801, Ireland was united with Great Britain and a new National flag was created to represent the three countries. The Cross of St Patrick, pictured above, was merged with the Union flag to create the Union Jack that we still know and use today.