It is an indoor plant called the aluminum plant... Pilea cadierei.  It is vining in nature.  The reason that you are seeing all the aerial rootlets along the stem is because the air in the container is humid.  This should be potted up in soil-less potting mix so it can grow, not just exist.  Put into a small container with a drain hole.

Since it has been a very humid atmosphere, after potting it up, put a clear plastic bag, like a sandwich bag, over the top of the plant like a tent that does not touch the plant.  Every day, leave the bag off for longer and longer periods of time so the plant can adjust to regular air humidity   If it is exposed to regular air constantly, it will turn yellow and brown and die..

Go online and look for information about the plant, searching on its botanical name which I have given you.  Growing conditions are bad currently and it is amazing it has lasted this long.