The original banana lacked the ability to reproduce. Apparently, the banana is the sterile result of cross-pollination between two very unpalatable species of fruit.
If the farmers of yore had not been so adept at agriculture, the lovable banana may not have survived to this day. These cultivators realized that while the banana seeds could not be planted for offspring, they could still bud the stems of the two parent plants together to grow the yellow plant. Through their efforts, the banana was introduced to audiences worldwide, and the Cavendish variety is now bought from markets and enjoyed worldwide.
A similar incident occurred with the seedless Navel Orange (which is actually a Siamese twin of fruits), but don't take my word for any of this. Read Matt Castle's article on damninteresting.com for a much more detailed account of the interesting origins of the banana.