Windows Phone, unlike Android and iOS supports two types of push messages: tile updates, and toast notifications. (Technically, there's a third type and the tile updates can be pushed from a server, pulled on a regular basis from the phone itself, or updated manually while an app is running.)
Live tiles are great for showing brief amounts of data (like the weather or a count), but not all apps deserve start page real estate. Additionally, toast notices that aren't noticed disappear from the screen after just a few seconds. What many folks who ask for a "notification center" are looking for is a "toast log" to see which apps received unseen toast notifications. We don't want to take away any functions related to live tiles, but we also want others to realize that a tile isn't a listing of missed toasts.
One of the internal arguments of our community is what form such a toast log should take. Is it another panel on the Start screen (notifications, tiles, apps list), an app that you'd pin to Start that would show a count of missed notifications, or a pull-down window shade like on iOS and Android. (I'm in the pinned app with counter crowd.)