How it works
Essentially it is a secure way of communicating over the web.
After some initial greetings and 'checks', the browser and server exchange a 'key' which is used to encrypt the sessions transmissions. If someone were able to intercept the transmission of say the contents of a form that contains credit card numbers, Social Security information, etc, they would not be able to decrypt it.
Part of the 'greetings and checks' is a digital certificate presented by the server to 'prove' that they are who they say they are.