To begin this discussion on the geography of Hyrule, it is vital to define exactly what the Zelda games mean when they refer to "Hyrule." There are several possible explanations, given the textual evidence. Hyrule is either a small kingdom within a larger world, a large region within a larger world, or the larger world itself. It is also possible that, at different times, the name "Hyrule" refers to any one of these three possibilities. Let's look at the evidence.
The logical starting place for our search is in the most distant past of Hyrule's history. The starting point of Hyrule's history is the creation of the world. The creation story of Hyrule, as told in the ALttP manual, the OoT manual, and in OoT, interchanges the words "Hyrule" and "world" freely. The ALttP manual also refers to the "world of Hyrule." Therefore, in the earliest days of the world, the name "Hyrule" was used to mean the entire world.
One might be tempted to end the discussion right here. But, as we shall see, the meaning of the word "Hyrule" changes over time. Since OoT is chronologically the earliest game in Hyrule's history, let's continue with evidence from this game. According to OoT,
Hyrule is a land rich in beauty. In addition to the Hylians, many diverse groups of people dwell in this country.
(OoT Instruction Booklet, p.7)
When Zelda first meets Link, she informs him that "[Ganondorf] wants to conquer Hyrule... no, the entire world!" This shows that, by OoT, Hyrule was seen as a region within the world, not the world itself. Since Hyrule is also a kingdom, the region is synonymous with the kingdom of Hyrule.
Next, let's consider evidence from a later time period. In the Oracle games, Impa tells Link that she has been sent from Hyrule to Holodrum and Labrynna. Holodrum and Labrynna are not referred to as being within Hyrule. Hyrule is a separate country, it's own independant kingdom.
The very first words of the story in the LoZ manual say,
A long, long time ago the World was in an age of Chaos. In the middle of this chaos, in a little kingdom in the land of Hyrule...
(LoZ Instruction Booklet, p.3)
So, in time, the kingdom within the land of Hyrule shrank. The borders of the larger "land of Hyrule" remained intact, but the kingdom within Hyrule no longer stretched to the borders of Hyrule. It is unknown where the borders of Hyrule lie, if indeed Hyrule has borders at this time. None of the in-game maps of Hyrule show Hyrule in it's entirety, since different games show different portions of the entire land of Hyrule.
The AoL manual's language is less precise, but is still informative. Page 4 refers to the "little kingdom of Hyrule," page 13 says that, "The vast Hyrule is the stage for the Adventure," and page 17 says that "Link Travels Again to the Land of Hyrule."
The evidence from LoZ and AoL leads us to the conclusion that in this later time period, the "land of Hyrule" was vast, but was not considered to enclose the whole world; and the action takes place in a small kingdom within the larger "land of Hyrule."
To conclude, let's summarize what "Hyrule" means in different time periods. At the creation of the world, "Hyrule" and the "world" are one and the same. By the time of OoT, the "land of Hyrule" is a vast region within the world, filled entirely by the "kingdom of Hyrule." In later times (ALttP, Oracle, LoZ, AoL), the "land of Hyrule" is still a vast region within the larger world, but the "kingdom of Hyrule" has shrunken to a smaller kingdom inside the "land of Hyrule."
Therefore, depending on the time period and the context, the word "Hyrule" means the entire world, a large region inside the world, or a kingdom within this large region. We have three technical terms: the "world of Hyrule," which only comes into play in the creation story of the world; the "land of Hyrule," which means a large region within the world; and the "kingdom of Hyrule," which means a kingdom within the large region. Usually the games are not precise, using only the word "Hyrule" to mean the "land of Hyrule" or the "kingdom of Hyrule."
To make things simple, throughout this article I will use the word "Hyrule" to denote the portion of the "land of Hyrule" located south of Death Mountain.