In cryptocurrencies, a transaction is the moving of funds (coins) from one address to another. Each transaction has a unique transaction ID that can be used to reference the transaction. In addition to the amount being sent, each transaction includes a fee that is paid to the miners for including the transaction into the blockchain. The amount of fee included in a transaction affects the confirmation time. A transaction is considered final when it has been confirmed.
Your Trezor device can be used together with the Trezor Wallet to make transactions for any of the supported cryptocurrencies. Your Trezor device is required to send transactions, as transactions are signed securely on the device itself - ensuring that your private keys never leave the device. Trezor Wallet also allows you to set a custom fee and add multiple recipients.
How do transactions work technically?
To understand how transactions work on basic technical level, check blog post Types of Bitcoin transactions: Part I, Part 2. More detailed description can be found in Bitcoin Wiki or in Bitcoin.org Developer guide.