If you look back towards the Medieval Era, you will find that the Medieval Church tended to be the most powerful institution in Europe. As you look towards the Renaissance, you'll find that it continued to maintain a great deal of power and importance, playing a critical role in shaping Renaissance culture.
For one thing, keep in mind that Renaissance artists depended on patronage, and the Church (with its wealth and power) proved extremely important on these grounds alone. This is reflected in the careers of Renaissance artists. Consider Michaelangelo, with his paintings of the Sistine Chapel and architectural work on St. Peter's Basilica in Rome, or Raphael's frescoes in the Apostolic Palace (to give just two examples).
In addition, though, one might also factor in the degree to which Christianity (and the Church) served as a landmark of Renaissance culture in and of itself. Remember, as a cultural artifact, the Bible and the various stories within it serve as a recurring theme for artistic depiction. (Here, we must note that there is very much a connection with artistic patronage: if the Church is commissioning artwork to be placed in a cathedral, for example, you should expect that the subject matter would be of a religious nature). Even so, it remains the case that Christianity had been the dominant religion in Europe since the Roman Empire and thus carried a tremendous and powerful cultural legacy in and of its own terms (a legacy reflected in the Renaissance itself).