Offline storage of crypto assets is explained in full under cold storage (of keys), which covers methods, set-up and risks. This page explains the plainer name and how it fits with related terms.
In crypto, "offline storage" means keeping the private keys that control coins somewhere that cannot be reached over the internet. The coins themselves always remain on the blockchain; what is stored offline is the ability to spend them. Common forms include a hardware wallet that signs transactions without exposing keys to the connected computer, a paper wallet with keys printed or written down, and computers kept permanently disconnected behind an air gap.
The industry tends to say "cold storage" for the same idea, by analogy with goods kept in a cold room until needed, while "offline storage" describes it more literally. The opposite is online storage, or hot storage, where keys sit on internet-connected systems so that funds can be moved quickly. Exchanges and custodians usually keep most customer assets offline and only a working balance online. The trade-off is convenience: offline keys are much harder to steal remotely, but they can be lost, damaged or stolen physically, so backups and secure locations matter as much as the device itself.