A tipping point is the criterion that must be met for the group to be able to complete.
For a Pay By Group where each person can specify his or her own contribution, the tipping point is an amount of money. In the below image, the tipping point is $250. Below that, you can see how much money is still needed to tip the group.
For a Pay By Group based around splitting the cost evenly among a minimum number of attendees, the tipping point is the minimum number of people the organizer needs to join the group, expressed in terms of "Sign Ups Needed."