Asymmetric encryption

asymmetric encryption (public private keys)

symmetric

padlock and key
the padlock and key come from the same owner - if you lock your document and send it to someone - you also have to send your key to that same person - thereby making it pretty pointless because you have to send the key in possibly the same insecure way as you did your document

mailbox and mailbox key
the mailbox is public, anyone can see it
only the owner of the mailbox key can open it
people who need to send stuff to each other first - share their mailbox address with each other (public key) - the sender sends to the receiver's mailbox - the sender locks the document in the receiver's mailbox - sends the document to receiver - receiver receives it, and can only open it with his own mailbox key (private key) - sending mailboxes around is safe - because people can only see the mailbox - they cannot see what's inside