In simple terms analogy I would say:

Public key is like your home address,
and Private Key is like the key with whom you open/unlock the door from your home.

You would not give keys of your home to strangers,
but your address is public for everyone, so that you can receive packages, letters, etc...

Main difference here is that if you lose keys from your home, you can break in and make a new key,
but you can not do same thing if you lose your crypto private key.
If you lose your private key, you lose your crypto so keep it safe and back up.