The answer shouldn't surprise you, my friend. It's the same reason you and I speak English even when we aren't residents of United Kingdom.
Colonization
It was back in the year 1492 when an Italian voyager, or should I say a monster, named Christopher Columbus reached a land the locals called Guanahani and he named 'San Salvador', presently called El Salvador in Central America. His voyage was 'sponsored' by the Crown of Castile, basically the modern day Spain to locate new lands and resources. The fool was intending to discover India, for its spices and riches. Even after reaching Salvador, he believed he had landed in some part of Asia.
Columbus found gold and silver, communities far more complex than the European cities. The inhabitants of the land were friendly and showed him directions to gold-rich areas, but Columbus had no intentions of making friends.
Here is an excerpt of what he documented.
"They (the inhabitants) ought to make good and skilled servants, for they repeat very quickly whatever we say to them. I think they can very easily be made Christians, for they seem to have no religion. If it pleases our Lord, I will take six of them to Your Highnesses when I depart, in order that they may learn our language."
Impressed by Columbus' findings, the Castile Empire sponsored three more voyages. Columbus' discoveries inaugurated the Spanish colonization of Americas. In the meantime, as with every form of colonization, there was deaths in millions in the region, women were raped, people were amputated and children were forced to slavery.
But the worst was yet to come that would erase everything America originally had. Around 1500s, there was a huge influx of warriors called conquistadors from Spain sent by the Crown. The Spaniards (just having finished a war against the Muslims in the Iberian peninsula) imposed a new religion in the region: Christianity.
European diseases that they brought with them(smallpox, influenza, measles and typhus) to which the native populations had no resistance, and cruel systems of forced labor), decimated the American population under Spanish control. After this, african slaves, who had developed immunities to these diseases, were quickly brought in to replace them.
The Spaniards were committed to converting their American subjects to Christianity, and were quick to purge any native cultural practices that hindered this end. However, most initial attempts at this were only partially successful, as American groups simply blended Catholicism with their traditional beliefs. On the other hand, the Spaniards did not impose their language to the degree they did their religion, and the Catholic Church's evangelization in Quechua, Nahuatl and Guarani actually contributed to the expansion of these American languages, equipping them with writing systems.
The inhabitants that were abolished weren't ordinary nobodies, but the Aztecs and the Incas who were eliminated from the lands that are now presently Mexico and Peru.
These new colonies were funding a fifth of Spain's total revenues.
At their peak, the Spanish Empire had almost whole of Western coast of America colonized. The stories how each area got conquered wasn't much different from the rest. The phenomenon was the same: the Conquistadors had reached a critical mass and like a chain reaction, more and more territories could be captured by them. The only resistance they faced was by the other colonizers: the Portuguese and the French.
The major objective of the conquistadors was to spread Christianity and not the Spanish language. It was generally believed that Latin should be used for conversion purposes, but many missionaries found that it was easier to spread understanding and faith in one or more of the native languages. Thus, Latin, Spanish, and native languages were all used simultaneously during the Spanish conquest of most of South and Central America (Ostler 2005). This mix of languages gradually brought about new forms of Spanish that were unique to the speakers in the Americas. By the time the conquered populations had liberated themselves from Spanish rule in the decades of the nineteenth century, these dialectical versions of Spanish had become the official languages of the population.
What do we largely mean by the term "Spanish"?When someone says Spanish restaurant, women, men, etc, do they mean belonging to Spain because of origin or Latin American because of spread of language?
In general, the term 'Spanish' in modern times only refers to the culture and people living in mainland Spain. The 'Spanish speaking people' from Latin America and Mexico are called 'Hispanics'.
Also, what are the various dialects or variations of the language and how are they different from each other?
There are many many dialects of Spanish since it spreads so widely. There is a greater difference observed in the accents, but there are also grammatical differences. If you are from India, you will get this analogy: The variations in Spanish are like variations in Hindi: Haryanvi, Bhojpuri, Urdu, Marwari. There are 'common versions' and 'High' versions: i.e. the language as is it is spoken and as it is written in newspapers and books.
