The task feed is a live stream of tasking that's going on across all callbacks in your operation.
This is located in the "Operational Views" dropdown.
When leading operations, it's nice to have an overall sense of what's going on across all of your operators and all of the callbacks. Traditionally, this is a pretty hard thing to keep track of and can quickly clutter your workspace. With a simple live task feed, you can monitor what's going on, click to see the results of any tasks, and stay updated overall.
You can also use the top right to filter down exactly what you're wanting to see such as: