There are some great answers in the FAQ

The best theory I've seen put forward is the relative low number of domesticated animals in the Americas. In the old world chickens, horses, dogs, cats, rats, sheep, pigs and dozens of other animals lived in close contact with humans. This gave a greater chance of diseases carried by these animals managing to jump to humans. The process is called zoonosis. This meant an overall greater number of diseases in the Old World than in the New World.

There's some debate about this one, but there's evidence that Syphilis originated in the New World, and was brought back. The first recprded outbreak of Syphilis was during the Italian Wars in 1494/1495, involving a more virulent and lethal form of syphilis. That time frame would line up well to early contact with the new world, and it is known that syphilis existed in the New World prior to the Columbian Exchange and that sailors who had participated in Columbus's expedition later joined Charles VIII's army. The timeline and movements make it plausible for syphilis to have been carried back from the Americas.

However, there is much debate about whether or not syphilis was present in Europe prior to contact with the Americas. There's some historical skeletal deformities that some historians attribute to the symptoms of tertiary syphilis and other historians hold the view that many syphilis cases were actually misdiagnosed as leprosy.

While there's no consensus for either side, syphilis is a good example of a disease that may have been carried back from the Americas by Columbus's journeys.