When iPhone first came out in 2007, it was the first device to include Visual Voicemail, a feature that allows users to view their voicemails, scroll through them, and of course listen to them, directly from the device. With Visual Voicemail, no need to dial a number and go through an automated message system to listen to your voicemails.
Since everything is now handled directly on the phone, you can also change your voicemail password directly from your iPhone.