On the rebranded OneDrive Blog Microsoft explains the thinking behind the new name:
Why OneDrive? We know that increasingly you will have many devices in your life, but you really want only one place for your most important stuff. One place for all of your photos and videos. One place for all of your documents. One place that is seamlessly connected across all the devices you use. You want OneDrive for everything in your life.
Here's a promotional video introducing the new OneDrive name:
The name change is the result of a trademark dispute with the British Sky Broadcasting, a UK-based satllite broadcasting and telecoms provider, which uses "Sky" as its consumer brand in a number of Europeann countries. Microsoft agreed to the name change after a UK court ruled that Microsoft's use of SkyDrive infringed in British Sky Broadcasting's trademark.
As part of the agreement Microsoft has agreed not to "pursue its planned appeal of the decision" and Sky will allow "Microsoft to continue using the SkyDrive name for a reasonable period of time to allow for an orderly transition to a new brand". The agreement also contains " financial and other terms", but the details are confidential.
SkyDrive, which Microsoft first launched in 2007, has become an increasingly important part of Microsoft's platforms. On Windows Phone the cloud storage service is deeply integrated into the platform (e.g. used for storing backups, settings, and auto-uploaded photos) and is also one of the locations for storing Office files. There's also a SkyDrive app for Windows Phone that provides access to additional files and sharing functionality.