What does asymmetric encryption mean?
Your answer: You need different keys for encryption and decryption.
Symmetric encryption is the "classic" encryption with which you use the same password for encrypting and decrypting (e.g. with ZIP archives, password managers in a browser of mail client). Symmetric encryption is usually not used for email (of course, you can send symmetricly encrypted files as attachments). If symmetric encryption is used for communication then both sender and recipient must ahve access to the same key.
Asymmetric encryption means that (using much more complicated mathematical methods that in the symmetric case) there are no single, independent keys but that always two mathematically related keys form a key pair: the private key and the public key. The sender uses the recipient's public key for encryption. The recipient uses his private key for decryption.
Asymmetric cryptography does not only allow encrypting and decrypting data but also signing (and signature verification) for proving that the respective person (or organization) has created / authorized / sent the data and that the data has not been modified after the signing.
public keys 

private keys 
