Bank web-sites are secure through HTTPS which encrypts the information. From Wikipedia:
HTTPS is a URI scheme which has identical syntax to the standard HTTP scheme, aside from its scheme token. However, HTTPS signals the browser to use an added encryption layer of SSL/TLS to protect the traffic. SSL is especially suited for HTTP since it can provide some protection even if only one side of the communication is authenticated. This is the case with HTTP transactions over the Internet, where typically only the server is authenticated (by the client examining the server's certificate).
The main idea of HTTPS is to create a secure channel over an insecure network. This ensures reasonable protection from eavesdroppers and man-in-the-middle attacks, provided that adequate cipher suites are used and that the server certificate is verified and trusted.
Web browsers know how to trust HTTPS websites based on certificate authorities that come pre-installed in their software. Certificate authorities (e.g. VeriSign/Microsoft/etc.) are in this way being trusted by web browser creators to provide valid certificates. Logically, it follows that a user should trust an HTTPS connection to a website if and only if all of the following are true:
1.The user trusts that the browser software correctly implements HTTPS with correctly pre-installed certificate authorities.
2.The user trusts the certificate authority to vouch only for legitimate websites.
3.The website provides a valid certificate, which means it was signed by a trusted authority.
4.The certificate correctly identifies the website (e.g., when the browser visits "https://example.com", the received certificate is properly for "Example Inc." and not some other entity).
5.Either the intervening hops on the Internet are trustworthy, or the user trusts that the protocol's encryption layer (TLS/SSL) is sufficiently secure against eavesdroppers.