In the hospital setting, containing things that could be a danger to the public is very important. When people come in with diseases, for example, they are quarantined if those diseases are highly contagious.
This is done simply to protect everyone else who may come in contact with them. In the past, this was used for things like smallpox, though this is not needed as often now since that disease has been eradicated in the First World.
Still, there are many contagious diseases in hospitals, and the institutions have an obligation to the people to keep them safe. They do this in a few ways, including the use of packaging materials. When tissues or instruments that may be contaminated have to be moved, they must be packaged in something that will hold in the germs as well.
The medical products packaging testing process is quite extensive, and the end result is that things can be moved by truck or by helicopter without being a threat to those aboard.