What's the big deal with iPhone UDIDs?

What exactly is a UDID? How it is used? Why did Apple deprecated its use by developers ? Are privacy fears unfounded?

• A UDID is a 40 character string of letters and numbers, sort of like a serial number, and uniquely identifies a particular iOS device, including iPhones, iPads, and iPod touches. The alphanumeric code looks completely random to people, but it is actually based on various hardware characteristics.
• Since a UDID can be used as a reference to a specific iOS device, it can be used to connect other kinds of data to that device. For instance, UDIDs are used to connect a device to an iOS Developer Account, which allows that device to install and test apps written by that developer before their public release. Connecting the UDID to a developer account also allows that device to install beta releases of iOS for testing. Apple also uses the UDID to connect devices to a user's Apple ID.