The description "thick provision" simply means that all the space that is required for the virtual disk files is reserved when the VM is created. The phrase "zeroed out" means that blocks on the physical storage device are formatted with zeros to overwrite any older data.
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Thick provision eager zeroed supports clustering features such as VMware Fault Tolerance, a component of VMware vSphere that is designed to provide high availability (HA) for enterprise software applications.
See also: VMware vLockstep