What was the connection between increased trade in the Mediterranean and artistic output during the Renaissance?

The short answer is: money! 

During the Renaissance, trade by sea and land brought luxury goods to Europe, which were then sold for a profit. Hauling the thousands of pounds necessary to meet market demand was very difficult to accomplish on land. Improvements in navigation and shipbuilding enabled traders to travel much more quickly to far off places with exotic goods (like spices, silk, and precious metals) and return with hardly any increase to their burden. Once they arrived in port, the people who had commissioned the journey (wealthy merchants) or the travelers themselves would in turn sell their goods at marked-up prices. The increase in trade not only brought wealth to the Mediterranean, "stimulating" the economy-- it also provided the wealthy with enough money to invest in the arts.

Patronizing the arts was a way for wealthy individuals to "build up" or invest in their own cities, and such conspicuous consumption drove competition among the elite. With regards to religious art of the Renaissance, many of the people to have such works completed did so as a way of improving their standing with the Church or perception in society. Especially in Italy, a wealthy man might drink, gamble, and visit sex workers, but he could essentially clear his name and moral slate by paying for a very expensive piece of religious art to be created.