Managing notification preferences
Open Preferences from the notification bell to choose what reaches you, and where. Changes save as you go — there's no Save button.
The grid
Each row is a category (things like Achievements, Billing, Account, Security, Classes & family, or Blog — the exact list can vary a little), and each column is a channel: In-app or Email. Switch a cell on or off to control whether that category reaches you on that channel. A dash means that category simply has nothing to send on that channel, not that it's locked.
Security notifications are always on, marked with a lock and "Always on." These cover things like password changes, so they can't be turned off.
Unsubscribing from an email
Every notification email has an "Unsubscribe from {category} emails" link in its footer. This only turns off that one category's emails — it never touches in-app notifications, and it never appears on Security emails, since those can't be turned off. Following the link asks you to confirm before it takes effect.
For everything else about your account, see Changing your account settings.