Authorize Only means that the payment is held from the customers account but, not yet transferred to your account. You can "Capture" the payment any time by generating an invoice via Magento. Capture will transfer the money to your account. This method is used in cases where an order is placed and the shipping is done separately. In this case you will want to capture the amount after its shipped.
Authorize & Capture means to immediately take the money from the customers account and transfer it to your account. In this case the invoice is generated automatically (unlike "Authorize Only" where you need to generate the invoice manually)