Subscriptions are your way of registering for a specific alert. When you subscribe to an alert you, or another employee has defined, a copy of the original alert is created, to which your subscription is linked. This way, if you modify one of your subscriptions, only your copy of the alert to which you subscribed is effected. Your changes are not applied to the subscriptions of other employees.
Editing a subscription does not modify the alert to which it is attached, it modifies the copy of the alert.
For example, if user A created the alert to which you are subscribed and modifies any of the properties, their changes are applied to your subscriptions, since you inherited these original alert properties when you subscribed to the alert.
You cannot edit subscriptions unless you are the owner of the subscription.