Answer:
by having an empire, stretching over half of africa, the americas, india and china, oceania and the middle east
It is a common misconception that the 'great' is a title indicative of 'greatness' as alluded to above, as the actual origin is from a mostly-unused meaning of 'great'. In the case of Great Britain the 'great' just means 'largest' since Great Britain is the largest island in the British archipelago*. It is a purely geographical term.
*A collection of islands off the North-Western coast of continental Europe, on which the Republic of Ireland and United Kingdom of Great Britain and Northern Ireland can be found.