I have provided examples from daily life since simply the difference between the types is a question that has been thoroughly discussed on the internet and on this site.
You put the document you wish to protect in a box with a lock and lock it with a key. Anyone with that key can open the lock and access the document. Usually this is used for protecting data at rest, so you are the only person with the key.
You put the document you wish to protect in a box with two keyholes.
You wish to send this box to someone, so you ask them for their lock-key (which is freely shared). You use it to lock the box, but you cannot use it to unlock the box and neither can anyone else. You can send this box through some untrusted messengers (post office or something) without fear of it being unlocked, as even if they got access to the lock-key, they can't unlock it.
Once the person you sent the box to receives it, they can unlock it using their own personal unlock key, sold to them by the manufacturer of the public lock-key.
In summary: the receiving party publicizes a key that can be used to encrypt data in a way that only themselves, with a given private key, can decrypt it. This allows the sending party to send encrypted data without having to send a symmetric (both unlock and lock) key through untrusted channels that may take it and decrypt the data on its way to the recipient.