It's quite simple really.
The Union Jack is the flag (jack) of a group (union) of countries.
Jack - A flag, containing only the union, without the fly.
Union - a composite of Saint George's Cross (England) and Saint Andrew's Cross (Scotland) and Saint Patrick's Cross (Ireland)
The flag is normally called the Union Jack because it represents a union of countries — England, Ireland, and Scotland and Wales (although the current flag does not include a flag from the latter).
The national flag of Wales is a red dragon on a background of white and green. Wales is not represented in the Union Flag because when the first version of the flag appeared Wales was already united with England, but the Welsh flag is in widespread use throughout that country.