Boats were a major part of medieval transportation. Without combustion engines or good roads, dragging loads along the land was very slow and inefficient. Much more efficient was to float heavy goods on barges. Every smooth-running river was full of boats and barges, carrying both people and goods. Bridges had to be built high enough that boats could easily pass underneath. The more expensive a trade good and the further distance it had come, the greater the chance that it had been on a boat.
Boats were powered either by manpower (rowing or poling), horse power (barges pulled along by a horse or mule on the towpath), or sail. Sailing on the rivers was mostly to increase one's current-fueled speed and to improve steering. Part of the reason the Burgundy region became a major center of wine-growing, even aside from its good soil and climate, was that it was easy to put wine barrels on barges and float them downstream to the large Paris market.
Sail really came into its own on the ocean. Sailing ships had been found in antiquity, but there were many improvements to rigging and sails during the Middle Ages. The boldest sailors, of course, were the Vikings. They developed their longships in the late eighth century, ships that could be either rowed or sailed, were big enough to cross the open ocean, and shallow enough to row up Europe's rivers to find tempting targets to raid. By the end of the tenth century, they had reached (progressively) Iceland, Greenland, and even what are now the Canadian maritimes. (See more here.)
Other than the Vikings, most medieval sailors were hesitant about heading off out of sight of land. Ships tended to hug the shoreline. Those heading to the Holy Land from Western Europe on Crusade usually went by ship, as both quicker and (slightly) less dangerous, though shipwreck on the windy and treacherous Mediterranean was always a possibility. At the beginning of the thirteenth century, when leaders of the Fourth Crusade were trying to book ship passage for their soldiers to get to the East, the Venetian ship-masters charged them such high prices that they had to accede to Venetian demands to sack one of Venice's trade rivals as part of the price. (The Fourth Crusade was a disaster all the way around, but that's a different story.)
The biggest advance in ships in medieval Europe since the Viking longships came in the fifteenth century. Prince Henry of Portugal, nicknamed "the Navigator," sponsored improvements in ocean-going ships that allowed Portuguese sailors to leave the well-known confines of Europe and the Mediterranean and start south along the coast of Africa. Henry's purpose was to find a way to get to the Indian Ocean, where spices from the fabled Orient came on Arabic dhows (ships), to join trade networks that led to Europe. He found Africa a lot bigger than he had anticipated, but quickly realized that trade and colonies in west Africa had a lot to recommend them in the meantime (ever wonder why Angola is Portuguese-speaking?).
It was of course due to rivalry with Portugal that led the Spanish kings Ferdinand and Isabella to sponsor Columbus and his crack-pot scheme to reach the East by sailing west. So the integration of the New World into European culture owes a lot of fifteenth-century ship building.