Since Dante and Boccaccio made the decision to write in the vernacular of their homes--in both cases,Tuscany--the language has been associated with literacy and culture. During another crucial moment in Italy's history, the Risorgimento, or the unification of Italy into a modern nation state in the mid-nineteenth century, Tuscan still came up on top as the dialect that would be called Italian. At a time when newspapers proliferated, like blogs do today, they all were written in Tuscan. The language of the newly-formed parliament and the Quirinal was also Tuscan. When Carlo Lorenzini wrote his serial installments for the newly-founded "Giornale per i Bambini," a newspaper based in Rome, which has its own dialects, it was still written in Tuscan. Out of this children's newspaper came the most widely-disseminated story to come out of Italy, "Le avventure di Pinocchio," which was written in the Tuscan dialect.
That has not changed even with movements to democratize culture--multiculturalism--in the modern world. The question of why Tuscan persisted as the dialect of choice for Italy is an interesting one, considering that the economic center of Italy has moved north of Tuscany and the political center is south of Tuscany. Tuscany's main role today is still as a symbol of cultural achievement of the peninsula in the arts: the Renaissance, after all, was born and matured in Tuscany. Out of tradition and convenience, Tuscan is the language of one of the newest nation states in Western Europe. Given how already culturally and politically fragmented the Italian peninsula is, it is doubtful that you will see anybody try to elevate regional dialects and diminish the importance of Tuscan as the preeminent dialect, or Italian, as we know it. In places like Catalonia in Spain where politicians attempt to replace the national dialect with the regional dialect, it often corresponds to an ideology of secession or separation from the rest of the nation. Language is very political indeed.
As far as which dialect becomes standard in a country, that is a big question, and the reasons can often differ. We shall look to the Iberian peninsula again for an example. Castilla, the part of Spain that gave birth to what we call Spanish today, was for the much of Spain's history a cultural and economic backwater of subsistence farmers and warriors raiding neighboring, richer regions. When Isabela la Catolica, who represented Castilla y Leon and Ferdinand who was the king of points east, united Spain under their standards, the dialect of these central realms was on its way to becoming "Spanish." No doubt what sealed the deal in Spain's case for the Castilian dialect becoming the national language was the conquest of the Americas. From Mexico to Peru, the natives were taught Castilian. Then the dialect of a minority of the peninsula became the language of the majority of the Spanish Empire. An interesting side note to this is that when Charles V, Isabel and Ferdinand's successor, was Holy Roman Emperor and King of Spain, he added Castilian to the list of languages he commanded, including Dutch and German, but he preferred to speak French. Historically, it has not been important which language the monarch has personally preferred; other forces shape which dialect becomes the national language.
In China, a place with hundreds of dialects, the dialect of Peking in the northeast corner of the empire, where the emperor put his capital, became the official language, "Mandarin Chinese" of the whole country. Until that choice was made, it was neither the geographical nor the cultural center of the country.
We can see how the reasons why the Tuscan dialect became the Italian language are cultural, rather than strictly economic or political. Generally, it does not matter what the language of the monarch is, however, or England would be speaking a dialect of French today and Spaniards would speak Flemish, German, or French. In contrast with Italy, in Spain Castilian became the national language of the Iberian peninsula for political reasons. On the other hand, in China, it was just a matter of which dialect was spoken in the city that became the capital of the Chinese empire.