BigE
There are several types, it depends. What most people are aware of a server certificates. These let others know that the site they are accessing is truly that site. But how? These certificates are signed by Certificate Authorities with CA certs. These are either distributed with your OS or can be imported carefully. If you trust the CA certs and they sign the Server certs, then you can trust that the connection is trustworthy.
That is the meaning of the lock box or icon to right of the URL box, if the connection is trustworthy. You can dive down and see the server's cert, the security params and which CA or CAs signed it (CAs can have chain of trust also).
Another use is to identify you to a host. These are used by enterprise systems to verify users. For instance the government CAC cards have a cert embedded in them. Other digital tokens can have certs built in. Things like this make it that the authentication requires they posses the device because the cert is on the device.
System to system connections are also protected by certs. The lets a system not use a password to connect, since some of these operations are automatic.
Ron75
It shows that your website is secure. This link will bring up the explanation of what they are.
Ron