I cant answer for more recent monarchies, but especially in the Ancient Near East it tended to emphasize a rulers control over particular regions(among other things), both to mark out specific prestigious conquests and areas of national or religious significance, for example this is the title of the Hittite King Mursilis from a letter to the King Duppi-Teshub of Amurru:

"his Majesty Mursili, Great King, king of the Land of Hatti, beloved of the Storm God, son of Suppiluliuma, Great King, king of the land of Hatti, hero."

The specific mention of the lands of Hatti(being the geographic, political and spiritual core of the Hittite Empire) connects the king uniquely to that area, tying him directly to the core Hittite national identity. The additional titles describing him as both the son of his father Suppiluliuma and being beloved of the storm god gives him both legitimacy in the sense of dynastic succession and religious support. These extra title basically indicated:

-specific symbolic control over notable areas

-political connections and relationships

-religious connections

-indicators of personal exploits or powers

The more titles you had, the more great and powerful of a ruler you were, heres a longer one to give you a idea:

"the great chief of Kheta, Khetasar, the valiant, the son of Merasar (mrAsArA), the great chief of Kheta, the valiant, the grandson, of Seplel (sApA[rwrw]), [the great chief of Kheta, the val]iant"

So, let's explain first what 'Emperor' and 'Empire' tend to mean in this context. An Empire is a state of multiple polities and often multiple nationalities, and a superior level title to a king or its equivalents. It was a way for a leader to express that they controlled a large, diverse territory, and possibly multiple 'kingdom' level titles. The history of this use really stems in the west from Charlemange, who originally utilized the title to help shore up his control over the numerous kingdoms he had brought under his fold (and of course, owes its earlier history to Roman Emperors, to which I suppose every western holder of the title is at least partly harkening back to). At any rate, why would Victoria claim the title of 'Empress' of India.

Well, the answer is pretty simple actually. In 1874, the rule of India by the East India Company finally and definitely came to an end. This was a process begun two decades earlier during the Sepoy Mutiny in 1857, where British control of the sub-continent was seriously jeopardized. When the British crown took over administration of the territory, this is basically what the picture looked like: http://2.bp.blogspot.com/_SIbeWkfuYJ4/SVY7Gplz0tI/AAAAAAAABsw/U0xsr1v5um8/s400/345e47a227076b.gif

Those orange states were not single entities, for the record, but were administrative divisions and contained many many seperate smaller states. British Rule in India was thus a mixture of direct rule, and what amounted to protectorates of quasi-independent Indian sub-states.

So, the rationale/purpose of this title was two fold. One, to put the stamp of royal (really British) authority over the substates of India and the scattered and diverse territories and people's of the Sub-continent, thereby linking them more closely to the British state, and second, to attempt to unite those disparate peoples in some way. It seems largely to have been the brain child of Conservative Prime Minister Benjamin Disraeli.

Of course, the title also served as a nice vanity piece to add to help put an exclamation point on the prestige of Britain and her monarchs. After all, Britain was one of the largest states in history, yet her monarchs were nominally lower in Rank than the Austrian, German, and Russian leaders. I would expect this played a large role as well.