I have two questions here.
- What does the cipher-text overhead means?
- Why we were suggested not to encrypts the plain-text itself instead just encrypts only the key (i.e random number)
OTOH, if you are referring to Hybrid Encryption as suggested in the comments, then this is the explanation - The advantage of PKI is that it does not require the 2 parties to share a common secretHowever, PKI is much more inefficient and slower than symmetric cryptosystems. A hybrid cryptosystem combines the convenience of a PKI with the efficiency of a symmetric encryption.
In hybrid encryption, the symmetric key to be used for the encryption is agreed upon using PKI, but the rest of the communication is encrypted by the symmetric key.
For very long messages, the bulk of the work in encryption/decryption is done by the more efficient symmetric-key scheme, while the inefficient public-key scheme is used only to encrypt/decrypt a short key value.