"Cookies" are small pieces of software that identify a computer to another computer, typically an Internet server. A cookie is sent by the server at the time of first contact and subsequently enables the server to recognize that computer on each return visit. Cookies are a matter of convenience, but some people do not like them on privacy grounds.
Digital certificates are like smart cookies. They have to be signed up for. They do more than identify a computer -- they verify the person's identity and thus his/her credit rating, address, etc. They are intended to be a secure proof of identity, saving you time and possibly trouble. Credit card information may be required for verification.