Last updated: October 2023 / 812222 o'block
Your Bitcoin hardware wallet does not need to be connected to your computer or the Internet for you to receive bitcoin. It works a little like email: it arrives to a specified address whether you are at that time logged into your email account or not, and it just sits waiting online for you until you are ready to do something with it.
Ok, that was easy. Now, if you are curious how it can operate this way, here it is in more detail.
You can imagine the Bitcoin network as a list of mailboxes (each mailbox corresponding to a Bitcoin address). If you have the keys to the mailbox, you can check what's inside or move it to a different mailbox. However, if all you need to do is receive a transaction - just as with email - you don't need to be online at the time of the transaction. And, to send you something, all the sender need to know is your receiving address. Technically, they aren't moving bitcoin from their wallet to yours, they are moving bitcoin from an address they control to one that you control.
Just as anyone can drop you an email so long as they know your email address, anyone can send you bitcoin so long as they know your receiving address. A difference from email is that whereas only you can view your emails, anyone can also see how much bitcoin is on an address. They can't spend it though (because they don't have the keys) and if you follow basic privacy guidelines, they can't tell whose bitcoin it is or how much you may have in other addresses or wallets.
If you want to receive bitcoin, you need a bitcoin address (it can take form of a string of numbers and letters, or a QR code). You get this from a software or hardware wallet (hardware wallet being the more secure option). Your wallet has your mnemonic seed phrase; based on the seed, it can generate private keys which control your public Bitcoin address. This address you can send to the person you want to receive money from. (You can even publish it online if you like for people to send you tips, for example.) When the sender send the bitcoin, what they really do is notify the network that they want the bitcoin moved from their address to yours and that recorded as a transaction on the chain.
An interesting aspect of this is that you can generate your receiving address (or many) at any time, perhaps long before you need to use them. You can then disconnect your hardware wallet, even wipe it (so long as you're keeping your seed by other means), and keep your receiving addresses in a text file or a photo on your phone, for instance. The receiving addresses will remain valid, operational if/when you need them, and once you connect or restore your wallet, you will be able to spend the bitcoin from those addresses.
Nothing in the wallet receives the bitcoin. Hide it in a deep dark place somewhere. Spend a nice day at the beach, take with you nothing but a towel, have a piña colada or something - meanwhile, the Bitcoin network will take care of the rest.
After the sender has sent bitcoin to your address (or to be precise: after a sufficient number of confirmations), the entire network now knows that on this public address there is an amount of bitcoin. They don't know whose address it is, or how to unlock your "mailbox"; if you've kept your seed safe, only you have the private keys that can unlock it. This is how your receiving transaction can be done without you doing anything, yet your money is kept safe until you are ready to use it.
You will need your hardware wallet to move or spend your bitcoin. It will use your private keys to sign that transaction.
What you do need your wallet for: creating receiving addresses, moving or spending your bitcoin.
What you don't need your wallet for: receiving bitcoin to your address.
Graphical abstract: for when you just need a quick overview or reminder - same stuff as above, just all in one image.
