Proof-of-spacetime (PoSt), usually used in reference to Filecoin, is that way that a storage miner proves that they are continuing to store a unique piece of data for the network.
PoSt is similar to proof-of-capacity in several ways: they both require participants in the network to have a financial incentive to participate honestly in the network, and have no benefit gained by harming the network. However, PoSt differs in that it lets network participants show that they have been physically storing data over a certain period of time. This is proved as randomly chosen miners will be selected and have their data read for verifications.
According to the creators of proof-of-spacetime, Tal Moran and Ilan Orlov, this is called the “’Rational’ Proofs of Space-Time because the true cost of storage is proportional to the product of storage capacity and the time that it is used.”