Creating new addresses
Trezor and other hardware wallets generate addresses in a deterministic manner, and they allow exporting a master public key (also called “xpub”) which can be used by other software to generate the same addresses. This is convenient because it allows receiving payments without direct access to the hardware wallet, you only need it for sending.
Obtaining information from a server
Bitcoin is a peer-to-peer network with no servers. If you’re running a node, you have information about every transaction that has ever happened. You can import the master public key into the node’s wallet and scan the blockchain for transactions associated with it.
