Some people have mentioned security...patching in particular. Containers won't help if you don't have patching down. At the very least it lets you patch in the lab and easily promote the entire application into production.
I think that the security arguments are a canard. By making it easier and faster to deploy you should be able to patch app dependencies as well. I, for one, would automate the download and install of the latest version of all libs in a container as part of the app build process. Hell, build them all from source.
IT departments need to be able to easily move applications around instead of the crazy build docs that have been thrown over the wall for years.