What was swapped from each of the sides during the columbian exchange? what did the “new world” (america) give to the “old world” (europe).

It is impossible to have a full list both because it would be too long and because some of the Columbian exchange might have happened undocumented, for example in the case of viruses.

But here are some examples:

The new World gave: potatoes, corn, tomato, vanilla, tobacco, syphilis bacterium,  guinea pig, avocado, cocoa,

The old word gave, among others, apples, onions and rice.