Until Update 3, Windows Phone 8 only allowed you to assign custom ringtones to individual contacts' phone numbers. But with this new release, you can now assign custom ringtones a contact's text messages. And you can use custom ringtones for many more things, including instant messages, emails, voicemails and reminders. The result is a far more personalized experience.
So there are two things going on here. The ability to assign custom ringtones to both calls and texts from individuals. And the ability to use custom sounds, globally, for instant messages, emails, voicemails and reminders.
Assign a text tone to a contact
In previous versions of Windows Phone 8, when you created a new contact or edited an existing contact in the People hub, you were provided with a single Ringtone option: this is the sound that would play when that contact called you.
With Update 3 installed, you can also add a custom ringtone or "text tone" to new and existing contacts. This happens, as expected, via that person's contact card (either while its being created or by tapping the Edit button while viewing an existing contact).
Custom sounds for instant messages, emails, voicemails and reminders
Additionally, you can now assign custom sounds for instant messages, emails, voicemails and reminders. These sounds will be used globally—i.e. for all instant messages, or whatever, and are not assigned on a contact-by-contact basis. As such, you configure these sounds from within the Ringtones + Sounds settings interface.
For example, if you peruse the options under New voicemail, you'll see all the original items—the built-in Windows Phone sounds, the Nokia ones if you have a Lumia handset—but you can also use your own custom ringtones. These will appear under a section called Custom.
Note: To add ringtones to your phone, use one of the Windows Phone sync apps. In the Metro version of this app, you just tap the Add to Phone button, choose Add Ringtones, and then navigate to the location of the files you wish to add.
In a related vein, developers can add custom sounds to their apps' toast notifications too.