Not all that long ago, thin provisioning became a feature that storage vendors were tripping over themselves to offer in their products. Since then, it has become a de facto standard that you'll find in just about any virtualized storage array worth its salt.
Unfortunately, the huge potential of thin provisioning is often overshadowed by the complications of using it in production. That's a shame.
At its simplest, thin provisioning grants more storage to a given consumer than you are actually reserving or allocating. This can be done on a SAN, but you'll also see it in various virtualization hypervisors, and you can potentially do both at the same time.
Let's say you have a virtualized file server that you've configured with a thin-provisioned 500GB virtual disk. That 500GB virtual disk is in turn sitting on a 1TB SAN volume that has also been thin provisioned on the storage array. The theory is that you'll merely use as much space on your SAN as has actually been written into that 500GB virtual disk. If there's 250GB of data on the file server, then only that much needs to be consumed on the SAN -- significantly better than having that entire 1TB tied up.