In 1606, the first Union Jack flag was created by merging the English flag (the red cross of Saint George) with the Scottish flag (the diagonal white cross of Saint Andrew on a blue background). Then, in 1801, the addition of Ireland to the United Kingdom added the Irish flag to the flag (the red Saint Patrick's cross). An image of the merger of the flags can be found online.
(The crosses on the flags relate to the patron saints of each entity - St. George is the patron saint of England, St. Andrew is the patron saint of Scotland, and St. Patrick is the patron saint of Ireland.)
The term "Union Jack" is attributed to various origins. The "union" is thought to come from the union of the three flags into one and "jack" has for many centuries referred to a small flag flown from a boat or ship. The Union Jack is most properly called the Union Flag, but that term is not as commonly used as Union Jack.
Today, Union Jack flag is the flag of the independent country that has absorbed England, Scotland, and Northern Ireland - the United Kingdom of Great Britain and Northern Ireland. The Union Jack is also incorporated into the flags of four independent countries of the British Commonwealth - Australia, Fiji, Tuvalu, and New Zealand.