I was going to write up my own explanation but this Wikipedia article pretty much sums it up.
Here is the basic concept:
Copy-on-write (sometimes referred to as “COW”) is an optimization strategy used in computer programming. The fundamental idea is that if multiple callers ask for resources which are initially indistinguishable, you can give them pointers to the same resource. This function can be maintained until a caller tries to modify its “copy” of the resource, at which point a true private copy is created to prevent the changes becoming visible to everyone else. All of this happens transparently to the callers. The primary advantage is that if a caller never makes any modifications, no private copy need ever be created.
Also here is an application of a common use of COW:
The COW concept is also used in maintenance of instant snapshot on database servers like Microsoft SQL Server 2005. Instant snapshots preserve a static view of a database by storing a pre-modification copy of data when underlaying data are updated. Instant snapshots are used for testing uses or moment-dependent reports and should not be used to replace backups.