What are symmetric and asymmetric encryption in the way Android interacts with the server?

Symmetric encryption means that the same key is used to encrypt and decrypt data. The algorithm in this regard is DES.
Asymmetric encryption, encryption and decryption use different keys. Before sending data, you must agree with the server to generate a public key and a private key. The data encrypted with the public key can be decrypted with the private key, and vice versa. An algorithm for this is RSA. Both ssh and ssl are typical asymmetric encryption.