Many big cities have their names preceded by Greater. Why not just Great? Does Greater indicate that the city is ambitious to expand itself?
Why is Greater not used for country names such as Great Britain? Is it just due to historical reasons?
In this context (greater Toronto) greater means “an area greater than the city itself” and “greater Toronto” is a shortened version of “the greater Toronto area”. Greater describes/modifies area rather than Toronto, giving a size contrast (greater) rather than describing the goodness of the city (great).
Great means big, greater means bigger.
So Greater Manchester is the larger metropolitan area around the city of Manchester in the middle.
However, Great Britain is the larger of the two separate and distinct Britains, the other being Brittany in north-west France. In French, Great Britain is Grande Bretagne and Brittany is just Bretagne. Brittany has also been referred to as Less, Lesser or Little Britain.
The answer is that the expression is based on how we, as humans, interpret geography. We refer to smaller, relatively unknown areas by the name of a larger, more well-known, area the smaller area is near.
By saying "Greater Toronto", we identify the city of Toronto and the smaller areas close by, at the same time acknowledging that these smaller areas are not, in reality, part of the city of Toronto. It is the same as saying "Toronto and its surrounding suburbs."
This nature can be observed when meeting someone unfamiliar to the area in question. If Sally lived in the suburbs of Washington DC, and met somebody from California at a conference, Sally would say "I'm from Washington DC", even though she lives in Falls Church, VA, and does not live within the boundaries of the city.
When someone asks me where I live, I would respond with "Charleston, WV" even though I don't live within the city limits, and the city is a 20 minute drive from my home.
In the phrase greater Toronto the adjective greater is not describing Toronto itself; the phrase as a whole refers to the urban area which includes Toronto. Thus it includes the small cities and suburbs within the entire built-up area in and adjoining the central city.
The phrase "great Toronto" would be taken as a description of Toronto itself. Great is a simple adjective; greater is a comparative. So the phrase greater Toronto is comparing Toronto to something else; the implicit something else is the entire urban area, which of course is larger.
Consider the list of any areas that could be referred to as "Toronto." Then, find the greater of these - the largest one. This is the "Greater Toronto area". This is in contrast to "Toronto Proper", which would be within the area defined in some document as explicitly being Toronto, and would not include outlying areas, even if they are just a kilometer from the border.