Your profile's Vanity URL is the web address of your profile. Just like your band's URL, it's the public view of your EPK. This will be index-able by Google.
You can click 'view profile' on the 'manage musician' page:
Step 1. Click 'musician' in the top righthand corner menu.
Step 2. Click 'view profile.'
This is the public view of your EPK.