https://www.elastic.co/guide/en/kibana/6.7/upgrade-migrations.html
This is pretty much the documentation outside of the details you can find in the PRs that merged it.
as for the task_manager index it's pretty much what the name says. It manages the running taks that can happen in Kibana, like monitoring, reporting and so on.
You can read more about it in the initial issue: https://github.com/elastic/kibana/issues/23632 and the related ones.