Anyone - If you select "Anyone" then anyone can make payment for a membership plan and join the group.
Moderated - Under a Moderated group, people would be able to enter their details and send a request to the Group owner, who can then screen if a person is right fit for the group or not. If a person is confirmed by the Group owner, they will then get an email with the link to make payment for the membership selected.
Note - If you select Moderated, all the membership plans become moderated. However, there is provision to make only selected membership plans moderated, instead of all. You can do this while creating/ editing a plan.