Sometimes groups can get a little bit more complicated. Every once in a while you'll run into a situation where everyone owes different amounts. For instance, if you're paying for a dinner, or doing a fundraiser, or taking a trip where people some people are staying much longer than others.
The flexible cost per person option allows all the members to specify their own contribution amounts, and is perfect for these types of scenarios.
The amount to collect is the total that you're gathering.
The minimum contribution per person field is an optional way to make sure each person pays at least a certain amount. For instance, say you're buying a block of tickets for a show, but some tickets are more expensive than others. You know the total, but each person will need to pay a different amount based on what type of ticket they want. However, all the tickets are at least $30. You can set the "minimum contribution per person" to 30 in this case, to make sure that nobody can claim a spot for anything less than that.