(This is very very medieval, and I'm more confident in modern, so we'll see how this goes! If someone more familiar with medieval Spain wants to fill anything in, please do.)

So the thing is that Iberian Jews were very much part of trade networks, particularly during the period of Ummayad Islamic rule from the 8th to the 11th centuries. They were part of large and extensive networks that stretched throughout the Mediterranean, and hundreds of years of documents attesting to the vast geographical scope of this network, and the involvement of Jews from many parts of the Mediterranean world, including large numbers from Iberia, are found in the Cairo Geniza. But that doesn't necessarily answer the question of how the Jewish population became so significant and so unique in the Iberian Peninsula.

In large part, yes, this is due to the relatively favorable environment which the convivencia, the mingling of Muslim, Christian and Jewish populations in Iberia, created, and a vibrant Jewish cultural and religious environment which ensued. Was this perfect? No. Under Muslim rule, Jews (and Christians) were still legally considered second-class and faced limitations and challenges (though in the early years of Islamic rule, they were often ignored in the interests of building the new nation), particularly during Almoravid and especially Almohad rule (in fact, when you mention Maimonides as being from Spain, he actually left as a child as a result of the Almohad invasion and spent most of his life first in Morocco and then in Egypt). But the opportunities which they were given not only by the relative tolerance extended to them but by the brilliant culture which they were able to be a part of meant that Iberian Jewry made a mark and developed a deep sense of pride.

The original Iberian Jews came in Roman times, and then faced a time of complete repression and persecution during Visigothic rule through the seventh century. Once the Visigoths were replaced by Ummayad Islamic rule in the 8th century, Jews faced many more possibilities and much better lives, leading to a large influx in immigration. Spain was unusual for Jews in that it was a multireligious and multicultural society, in which they weren't a small minority amidst a majority population. Does convivencia, with the implication not just of coexistence but of peace and harmony, really hold up? Not necessarily. Jews were often caught between the two larger groups of Christians and Muslims, which could be a chaotic existence, but it also led to unprecedented opportunity, especially in its earliest years post-conquest. The caliph, Abd Ar-Rahman, chose Cordoba as the capital of the kingdom of Andalusia, and he and his descendants worked to turn it into a center of culture, imitating Baghdad, from which the Jews of the kingdom were able to benefit and blend into Muslim society.

As residents of this Muslim kingdom, Jews were able to travel and trade very freely throughout the Muslim world, and participate in trade networks expanding outward into other parts of the world- like Europe and the Indian subcontinent- as well, often becoming quite successful and even wealthy. While Christians and Muslims of course traded as well, often Christians would have trouble trading with Muslim lands and vice versa- but Jews were able to bridge this gap by being neither of those things, as well as by relying on common relations and language with fellow Jews. (Indeed, in many ways Jews were serving the same role locally in Iberia, acting as a bridge between the Muslim and Christian camps.) Though trade and travel were dangerous, they also became a tool for Jewish success and acculturation, leading to the growth of the community through immigration.

At this early stage, Jews were still in the Jewish intellectual orbit of the Jews of Bavel, or Iraq, and would write/travel back and forth; however, soon the relative freedom of what would become known as the Jewish Golden Age of Spain led to a vibrant Jewish culture of Iberia's own developing. A yeshiva, or religious academy, was established in Lucena and became a source of pride for Iberian Jewry, but it was in Cordoba that the Golden Age of Hebrew poetry (both ritual and secular) and grammar began, with Dunash ibn Labrat and Menachem ibn Saruk both (at different times) part of the entourage of Chasdai ibn Shaprut, a Jewish physician and confidant of Abd Ar-Rahman III who was appointed by him as a statesman and as the nasi, or head, of the Andalusian Jewish community and who was the patron of a variety of Jewish scholars and intellectuals, cementing Iberian Jewry as its own entity independent of Bavel. First Menachem and then Dunash was his court poet, as was customary in those days, and they began what became an incredibly creatively fertile period in Jewish literature, influenced heavily by the Arabic poetry of the time.

Perhaps at the apex of both the ability of Jews to gain power and to produce creatively came Samuel ibn Naghrela, or Samuel Hanagid, who was not only one of the leading Jewish poets and scholars of his era but eventually became vizier of the kingdom of Granada, an astoundingly high level post for a Jew to attain anywhere in the world at this time. By this time, the Ummayad Caliphate that had ruled Spain had disintegrated into many smaller kingdoms, which, while making Jewish life more volatile (especially with new attempts at Christian reconquest of Spain), also gave Jews more of a chance to achieve higher ranks and roles. While ibn Naghrela was often challenged in his position, he became a prominent ruler in Granada and in turn a leading patron of Jewish intellectualism, as well as owner of a large private library. That said, while ibn Naghrela's Torah scholarship and poetry survived, his political influence did not. While he was well integrated culturally into Muslim society, he perhaps grew too confident in his role as a Jew in a Muslim role, or at least his son Joseph (who succeeded him) did- in 1066, increased Islamic religiosity in Granada led to a massive pogrom against the Jews of that city in which Joseph was deposed and crucified and thousands of Jews were murdered. While Jews were given the opportunity to rise, and often lived in security, the penny could always drop.

Interestingly, despite the fact that by many measures this is when the "Golden Age" ended, many of the most famous Jews of whom one thinks in the context of Iberian Jewry actually lived in time periods in which Christian culture was already on the rise, with Jewish ability to live in equality with Muslims lessening with the ascension of the Almoravid, and then the Almohad, caliphates. For example, Judah HaLevi, the legendary poet, came of age at the height of convivencia but faced its end upon the rise of the Almoravids and would spend his life in both Christian and Muslim Spain. Benjamin of Tudela, who you mention, was from Christian Tudela, in Navarre. Many Jews were welcomed by Christian rulers to their kingdoms as the reconquista ensued, given their connections in trade and subsequent economic benefit to their host country, and often, those who did not go to Christian lands would emigrate to North Africa (as Maimonides and his family did in the wake of the violent invasion of the Almohads). But those Jews who went to Christian Spain brought with them the influence of the intellectually stimulated, confidently equal Sefardic society which had been cemented into the Iberian Jewish psyche, and this led to many of the effects of convivencia Spain continuing to exist even as actual convivencia was falling apart.

By the time Iberia was overwhelmingly Christian, though Iberian Jewry became more closely acquainted with the Jewish communities of the rest of its European neighbors, the identity of Iberian Jews as being of Sefarad, which they considered a mark of greatness and elite status, was still strong. Overall, Jews felt Spanish in a way that a Jew in the same era in France would never have felt French (though of course modern analogies of national identity don't quite align). This sort of identity and cultural memory of their community's past greatness persisted even once their ability to maintain it was breaking down with increased persecution as the centuries went on. This very acclimated community with its clearly defined sense of place, therefore, became probably the first one in which, when faced with the quandary of "convert to Christianity or die," many chose to convert. And when those who would not convert were expelled, that same sense of communal origins and pride was maintained and became so strong that these expelled Jews often completely revolutionized the communities where they settled, turning them, in a sense, Sefardic. It's a very remarkable sense of cultural identity.