An approval point is like a checkpoint in a case, and is often used when the user needs to ensure or check something before moving on to the next step. The point is created in the process and cannot be edited or administered from the case itself.
The most common setting is that the approval points need to be approved in order, which means that the point needs to be approved before you can proceed to the next step in the case.
If the user has the right to approve the point himself, the button to approve will be visible and clickable.
If, however, the user does not have that right, they will instead only have the option to "Send notification for approval".
When you click on that button, a list of the users who can approve the point will appear. Here you have the option to check / uncheck those to whom you want to send the notification.
Once the point has been approved by the user, you can proceed to the next step.
You choose who can approve the approval points when you create your process and depending on which rights you assign to your users.
When the point is approved, it will say who has approved it, and the next step in the case is unlocked.