I don't know why I even started typing this answer as my knowledge is so scant, im only going to make myself look stupid, but here goes...
Basically SSL Server certificates combine 2 principles which are of benefit for the process of security between 2 remote parties on the internet.
The first is to prove the identity of the certificate holder, and the second is to encrypt the traffic using public key cryptography.
Starting with the second;
public key cryptography is a form of secrecy for data that involves a 2 part system in which there is a private secret key, and a public key. Anyone can use public key to communicate securely with the holder of the private key and this is good, and vice versa, because then no one can steal your credit card details.
However this doesn't guarantee the identity of the other party - when you put your credit card details into the web page, you not only want to be sure that no one on the internet can see it, you also want to be sure that the recipient is actually who they say they are, such as amazon or playboy tv.
The SSL server certificate is signed by a certificate authority that you have elected to trust by virtue of the fact that you trust microsoft, who have installed root certificates into your browser that they in turn trust.
So in summary a server certificate is essentially a proof that someone you trust implicitly, trusts them explicitly.
(and the certificate contains the other parties public key which you can use to encrypt stuff)