To reiterate the basics of the service, Apple Music will cost $9.99/mo for one individual, or $14.99 for a family of up to six members. As soon as you sign up, you'll be granted three-month free trial, which is hugely enticing versus the competition (though Spotify does regularly offer new users 3 months for $0.99/mo).
Even if you have no interest in the bulk of the service, perhaps because you are already enjoying similar service from someone else, there are still some compelling features. Beats 1 radio is one of those, as it's completely free to tune into. The same goes for Connect, which is how artists will communicate with their fans. Further, you'll also be able to listen to certain radio stations that are ad-supported.
If you happen to be a Beats Music subscriber, you'll be prompted to migrate your account the first time you open the app after Apple Music launches. Fortunately, all of the playlists you've created or subscribed to will be ported over.
It seems certain that Apple Music will kick off with enormous success given its free trial, so we'll still have to wait a few months before we learn how many people actually decide to stick with it afterwards.