What is the Union Jack?

The Union Jack is technically a maritime flag, used to distinguish British ships. It is also popularly used to describe the the flag of the United Kingdom.

The flag is composed of symbols of the constituent parts of the UK. The red cross at the centre is the cross of St George representing England. The blue Saltire flag is for Scotland, the red dragon Wales and the crown over the red cross is for Northern Ireland

UK? So why Team GB?
The Olympics brings to the surface the confusion created by the terms Great Britain and the United Kingdom. Great Britain should only really refer to the core island of Britain, not the outlying islands or Northern Ireland. It would, therefore, be more logical to have a team UK.

Uncertainty is also evident in the use of flags, anthems and other national emblems. Football supporters, for example, associate God Save the Queen with the England team, despite it being the national anthem for the entire kingdom. The confusion comes from the UK unusually having its constituent competing separately in football - a historical legacy of the role of English Football Association.

Rallying to the Union flag requires a suspension of normal friendly(ish) rivalries between the countries it represents.