A Programmable Infrastructure is any compute and storage infrastructure, that can be instrumented via application programmable interfaces (APIs) in an automated way, usually through Infrastructure as Code frameworks.
As oppose to classical infrastructures that requires manual operations, like installing a new server rack or adding a new storage disk.
Programmable Compute Infrastructure can be fully automated, up until a point where no manual maintenance is required - resources can be provisioned and removed based on use, automatically replaced on failure and even predictively allocated based on Pervasive Telemetry.
Programmable Storage Infrastructure, is harder to do, since moving of storage is not instant (unless preemptively mirrored - which is hard in itself), but at least provisioning and removal on demand is easily feasible. Planned maintained operations, that require swapping out the compute component of the storage infra, are equally trivial.