Online commerce has grown to be larger in value than in-store commerce in certain markets. The convenience of online shopping and trading is a core competitive advantage for merchants and popular with consumers.
To purchase online using a debit or credit card, you are expected to have the information that relates to the card account. Some service offer to capture and store the details for your convenience, allowing to shop without having to enter card details for each transaction (this is discouraged).
When doing online transactions, the physical presence of a card is not required. Information, as contained on the card is. This information is typically the card number, account holder name, expiry data and the CVV. All of this information could be provided if known, without needing to have a card present.
Depending on the service being used, different levels of authentication may be required before authorising access to the service.
This is not really directly related to you bank card. To do online banking you access your bank account directly and authenticate yourself directly with you accepted bank credentials and authenticators.