Apache SSL Public key/Private question

Hi everyone,
I have a quick/newb question:

I know that a public key is used to encrypt data and a private key is used to decrypt data but who keeps the public/private keys??

Does the Web Server hold both?
Does the Web Server have the public key and does the client have the private key?
Does the Client have both?

When I create a key using the openssl command (e.g. openssl genrsa -des3 -out server.key 4096) is that the private or public key??

Please help, thanks.

server use private key
client download public key automatic if client log into https .