The press release from Verizon says that "In one click, customers can start to explore their account activity quickly and easily, and complete popular transactions, including viewing a bill, managing Friends & Family®, changing an address, adding a new line of service, or activating a new phone."
The features of their 'Express Services' are nothing new, but accessing those features on the app should be far quicker than with the previous version or your mobile browser.
My Verizon Mobile will be available on all current Android devices, including Motorola's DROID, DROID X, and DROID 2 (R2-D2 edition also); HTC's DROID Incredible; the LG Ally; and the Samsung Fascinate. Owners of the aforementioned devices will be prompted for an OTA update containing the app.
Verizon also says that the features will later be extended to their customer service line. We assume this means that the customer service menu options will be simplified and streamlined for popular account management features.
source: Verizon Wireless