This only applies to organisations that have configured the option for a full, or partial approval process.
If a member places an order (for a subscription product, or for an event which is not configured as an open event) AND there is a member in their group who is not authorised, they will be prevented from completing their purchase until that new member is approved.
Administrators who have creator or operator roles, will receive the new membership applications report email, notifying them that a membership application has been placed.
To check that this is the case, go to the individual member's page in the admin panel. You will see the other members of the group listed in the top right hand corner of the page. Click on each of those members, and then check in the top left corner whether they show as being authorised or not.
Click here for details on how to authorise the new member.