Definition. An optimisation technique in which a shared resource (typically a memory page or a filesystem block) is only physically copied when one of its users writes to it. Until then, all parties share the same physical memory. COW saves resources in fork(), container layers and modern filesystems such as Btrfs and ZFS.
Why it matters. An elegant optimisation with security pitfalls: COW flaws in the kernel (Dirty COW, Dirty Pipe) have been exploited several times to gain write access the attacker should not have had. Anyone who reads kernel patch notes comes across the term regularly.
Related. Page Cache, Kernel LPE, CVE