A hardware wallet is often described as storing coins offline, which is misleading. It stores keys, and its defining behaviour is that those keys never leave it, even while it is being used.
The division of labour
The connected computer builds the transaction, holds the network connection and broadcasts the result. It does everything except possess the key.
The device receives the unsigned transaction, produces a signature using a key held in its own memory, and returns only that signature.
A key that is never transmitted cannot be captured by software on the host, which is the entire security argument in one sentence.
Malware on the host remains a real threat
Because the computer constructs the transaction, compromised software can construct a different one from the one the user intended.
It can swap the destination address, alter the amount, or substitute an approval that grants a contract access to token balances.
The device will sign whatever it is given if the user confirms, so the protection is only as strong as the confirmation step.
The screen is the security boundary
This is why the device has its own display and buttons. The details shown there come from the transaction the device is about to sign, not from the host.
Checking the destination address on that screen, rather than in the browser, is what defeats the substitution attack, and it is the one step users most often skip.
Devices without a display, or ones that rely on the host to show the details, lose this property regardless of how well their key storage is built.
Contract interactions are harder to verify
A simple transfer displays an address and an amount, both readable. A contract call displays function data that means little without interpretation.
Firmware for common contract types can decode this into a readable summary, but coverage is incomplete and unfamiliar contracts fall back to raw data.
Blind approval of unreadable data is the residual weakness of the whole model, and it is the reason unlimited token approvals remain a common route to losses even for hardware users.
Physical possession is a separate risk model
Secure elements resist extraction of keys, and a device PIN limits what an ordinary thief can do with stolen hardware.
None of that protects against a compromised supply chain, which is why devices should be initialised by their owner so the recovery phrase is generated on the device and never seen elsewhere.
A device supplied with a phrase already written down is not a wallet. It is somebody else's wallet that you are being invited to fund.