An offline device means to me something like a Trezor..
Most people can not know this. Example of cold wallets are Electrum or Sparrow wallet created on an airgapped computer, or airgapped hardware wallet like Foundation Passport, or a paper wallet that you generated on an airgapped device. Not all hardware wallets are airgapped.
How can a transaction be signed on an offline device and why that is needed?
Read this:
https://electrum.readthedocs.io/en/latest/coldstorage.html as an example.