Dockerfiles for dumb-init on top of various OS dockerfiles.
There are automated builds of these Dockerfiles in the following repositories on Docker hub:
These will be updated each time this repository is updated or the underlying images change.
I think this is best covered by forwarding you to the dumb-init documentation or the blog post introducing it. For some more general reading on why your containers should be using an init system see this post from Phusion which explains the technical details.