A pooled task is a task in your workflow that has a swimlane that consists either of a group or multiple people.
Each task in your workflow has a swimlane associated with it. The swimlane determines who will be assigned the task when the task is routed to. If the swimlane consists of a single user, then the task will automatically be assigned. This is the usual case. When a workflow is assigned, it shows up in the "Assigned Tasks" view of your task inbox.
However, there will be times when you will want to route a workflow to a group of users.
For example, you may have a team of designers who handle web content for your web site. You may not know ahead of time which one of them will perform the work needed. By setting the "designer" swimlane to the "designers team", everyone on the designers team can received notification of the task at the same time. And anyone who is available can claim the task to work on it.
This mechanism is collectively referred to as a "pooled task". A pool because it is sent to a pool of users. And only one of those users can then jump in and claim the swimlane. (Yes, the people who came up with these terms were adept at using colorful and poetic language)
At any rate, when someone from the pool "claims the task", they become the assignee. The task is assigned to them. At that point, the task appears in the assigned user's "Assigned Tasks" view of their task inbox. The other members of the team will still see the task but they will see that it is being worked on and they will also see who is working on it.
Pooled tasks are unique in that they maintain a notion of "delegates". Delegates are other people in the pool to whom the task could be assigned. When a pooled task first comes around, all members of the pool (team or group) are delegates. Any of the delegates could work on the task.
When someone finally does "claim" the task, they become the assignee. The delegates now consist of all of the remaining members of the team or group. At any point, the assignee can "unclaim" the task at which point the task will be transitioned back to being available for any of the delegates to pick up and work on. Alternatively, the assignee may "delegate" the task to any of the remaining delegates. Delegating the task re-assigns the task to someone else from the team or group.
In this way, the team can coordinate as resources permit to ensure the task gets done.
The workflow history captures all of these claim, unclaim and delegation events so that you can keep track of who worked on things. Pooled tasks (or participants nodes in the workflow model with a team/group in the swimlane) provide a way for a set of users to collaborate when availability isn't entirely known ahead of time.
To learn more about Workflow, please check out our Workflow documentation.