Good question. An iteration is a marker to generate velocity.

All of the points collected in that week are summed together and the average of those points across a configurable threshold (typically 3 weeks) is the velocity. Once you have a velocity, you can start to make predictions about the future.

For example, if velocity is 10, that means 10 points worth of stories can fit into an iteration. If the PM moves another story into the iteration, the last story would be automatically pushed into the next iteration. Makes it easier to answer the question of 'when will a story be done?' as well as 'how will changing the flow of stories affect deliverables?'

Highly recommend you read the documentation, it has been formed over many years and is excellent.

https://www.pivotaltracker.com/help/articles/quick_start/

Because then we'd call them weeks and Sprints would be Fortnights :)

In all seriousness I'm curious about the story pointing. Does the team meet together for that at Pivotal?

Repeated from above:

Pivotal has 3 regular meetings: daily morning standup (short), iteration planning (monday), retrospective (friday).

Any new stories during the week that haven't been pointed get pointed in the morning meeting.

Sounds like Pivotal combines elements from scrum and kanban in a way that works well for them. That's what you're supposed to do with agile -- keep adjusting the process until it's working well for your organization.

this ^^^^^^^^^^^