"The disk is offline because it has a signature collision with another disk that is online"

The Disk Signature is simply an ID number that is written onto a hard drive so that each drive is uniquely identifiable. Its original purpose was to allow the operating system to distinguish between drives on a software raid configured machine. On traditional MBR hard drives it is written by Windows onto the first sector and it was made standard procedure for Windows to check signatures during bootup and if duplicates were discovered they would be automatically replaced. In most circumstances this would not cause any serious issues and could often go completely unnoticed. If you want to know more about the disk signature then we suggest this article as the place to start.

From Windows Vista on-wards the Disk Signature acquired a new function and importance when it was made a part of the Windows operating system boot process. This means that in normal circumstances a lost or changed disk signature will result in an unbootable machine. The old way of dealing with duplicate signatures needed to change and so from Win7 the situation is handled differently and nothing is altered automatically during boot-up. Instead Windows will now essentially isolate one of the duplicate hard drives by not mounting it or any of its partitions in Windows, thereby forcing you to investigate the problem before deciding on a course of action. If you only have two drives then it will be the non-boot drive that will be fenced off and show in Disk Management as 'Offline'.
Disk signatures are randomly generated and so under normal conditions the chances of seeing duplicates are vanishingly small. It is the increasingly common practice of cloning entire hard drives, usually for the purpose of upgrading to an SSD or just a larger HHD, that is the cause of PC users encountering this problem. When a full and faithful sector-by-sector copy of a physical hard drive is carried out then duplicate signatures will result. Another way signature collisions can occur is with the creation and use of Virtual Hard Drives (VHDs). If for example a physical drive is converted to a VHD, or a copy is made of an existing VHD, then signatures will be duplicated and clashes can occur just as they do with physical hard drives.