A hardware wallet, also referred to as a signing device, is a physical storage device designed to generate and store public and private keys offline, as well as sign transactions.
Despite lacking some of the functionality of other wallet types, it offers improved security and simplicity for a minimal attack surface. It works alongside other wallet software as an external device: it creates and stores the keys, derives the Bitcoin addresses used to receive funds, and signs transactions when you spend. The software on the other wallet types handles all other tasks.
Recommended Bitcoin hardware wallets: Blockstream Jade, Coldcard, BitBox02.