Explanation 1:
MSC stands for Mass Storage Class. When your player is in this mode, the computer will see it the same way it would see a flash drive, as a removable disk. It will assign it the first available drive letter, as well as one for the memory card (if applicable). This is probably the more popular of the 2 modes, and is a more "open source" type of standard. Most comptuers detect the player in this mode without a problem.
MTP stands for Media Transfer Protocol. It is a Microsoft standard and is Microsofts solution to connecting digital players and cameras to a window based platform. MTP mode must be used in order to transfer ANY Digital Rights Managment (DRM) protected content. Services like Rhapsody and Napster will only function in this MTP mode.
Explanation 2:
The MSC mode of the USB stands for Media Storage Class mode and the MTP mode is Media Transport Protocol mode.
MSC mode will only work for MP3 files and WMA files without DRM (digital rights management). Essentially, MSC mode looks like a detachable hard drive to the computer. Many car audio players and home stereos that are compatible with MP3 players are expecting an MSC mode MP3 player for hooking up via USB. MSC mode may also support plain old data files.
MTP mode is for MP3 files and WMA files with DRM (digital rights management). These WMA music files with DRM including purchased downloads and (maybe) subscription music tracks require MTP to transfer and update the DRM licenses. MTP mode is required for use with subscription music services such as Yahoo Music Unlimited To Go, Rhapsody To Go, and Napster To Go.