Okay, so imagine you live a long time ago, before Christopher Columbus sailed across the ocean and "discovered" America. But imagine that other people knew about America already, even though they lived far away.
Some people think that there might have been trans-oceanic contact in the past, which means that people from different parts of the world might have traveled across the ocean to visit each other. This would have been really hard to do without modern boats and navigation tools.
There are different theories about this, but some people think that there might have been contact between Asia and North America, or between Africa and South America. They think that maybe people from one place traveled on boats to visit the other place, or maybe they got blown off course by a storm and ended up in a different place.
Some people also think that there might have been contact between Ancient Egyptians and Native Americans, or between Vikings and Native Americans. These theories are less accepted by historians, but some people still believe in them.
So basically, the idea of pre-Columbian trans-oceanic contact means that people from different parts of the world might have visited each other a long time ago, even though it was really hard to do.