A public key is an address (or a "wallet address"), a string of code, that others use to send money or assets to you. It allows you to receive assets from the senders.
As for a private key, it is an address that you use as a key to unlock the transactions in order to receive the assets that are transferred to you. However, when you use the services of an exchange, you will not be provided with the private key as your public key (or "a wallet address") of each token will be automatically paired to the exchange's private key. Thus, when someone is transferring a token to you by using the correct wallet address of yours, the token will be credited to your account where you can withdraw, store, or sell the asset directly without filling in any information to 'unlock' the transaction before receiving the transferred asset.
The only one who knows the private key should be the owner of the private key, otherwise, other people can use the account to send money to others. To have a clearer picture of this, imagine a vending machine that anyone can put money in, but cannot take money out of because they do not have a key; the only person who can take money out is the owner of the vending machine. In this situation, the vending machine acts as a public key to which people can send money, while the machine owner has a private key that allows access to the money.
For more information with interesting screenshot examples, please visit Plearn-D KUB EP.8: Private & Public Key.
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