I would say that the Renaissance can be considered a golden age because it was a time when Europe experienced a boom in arts, science and culture. Because of this, it was a time when things were better in Europe than they had been before (at least in terms of these things).
During the Renaissance, many new technologies emerged that changed people's lives. One major example is the printing press. This allowed more people to be exposed to more ideas than was previously possible.
At the same time, there were all sorts of great artists creating masterpieces of art. By creating these great works, the artists contributed to a time that was richer in culture than any time before (and perhaps any time since).
So this was a golden age because it was a time of major advances in various areas of culture. It was a time that was more advanced than times before and that makes it a golden age.
I do not exactly agree with the notion that the Renaissance was a time that "was richer in culture than any time before." It would be difficult to argue that it was not more advanced, since the creative arts and technology tend to become more sophisticated with time.
The Renaissance was a "rebirth," as its French-derived name defines it, of the Classical era. The writers, artists, and philosophers of the time hoped to revive an interest in progress that had been stalled during the Middle Ages.
Humanism, which we could say gave birth to all major philosophical movements that emerged thereafter, was a system of belief which encouraged rational thought as the key to solving most of the world's problems. It placed the human mind and its ideas -- not the Church or even God -- at the center of cultural life and production.
Though recent scholarship is changing our view of the period we have long called "the Dark Ages," one cannot deny that there was relatively less artistic innovation during the period, high rates of illiteracy, and an unwavering faith in the Church. Johannes Gutenberg's printing press was invented during the Renaissance. This, along with Martin Luther's insistence that everyone should have access to the Scriptures rather than having the Bible dictated to them, allowed believers to interpret Christianity for themselves and to have their own relationships with God. Inevitably, this led to questions about the Catholic Church's supposedly infallible authority and, eventually, less tolerance for certain corrupt practices, such as torture, which had gone unquestioned during the Middle Ages.
Another "golden" aspect of the Renaissance, though less often discussed, is the rise of the merchant class. Beginning in the thirteenth-century, which is considered the early Renaissance, a middle-class was established in Europe, due to initial ventures in trade. Geoffrey Chaucer's "The Canterbury Tales," was the first romance written to appeal to literate people of different classes. Previously, romances were told to and written expressly for the entertainment of nobles.
The rise of the merchant class is evident in a great deal of artwork commissioned during the Renaissance. Consider, for example, one of the most famous: "The Arnolfini Marriage," also known as the "Arnolfini Portrait," by Jan van Eyck. It depicts Giovanni di Nicolao Arnolfini, an Italian merchant, and his wife in what was probably their home in Bruges, Belgium. Their clothes, their home decor, and the well-groomed little terrier at their feet tell us that these are people who live well. Like the Medicis, the Arnolfini family became a powerful political family, albeit in a much smaller town, as a result of their success in business.
Thus, the Renaissance can be considered a Golden Age due to its revival of Classical ideas, its emphasis on rationalism, the diminished power of the Church in favor of individualism, and the rise of the merchant class.