Why are chips safer than magnetic stripes?

The answers to the above question explain that the chip based cards can not be cloned as the "secret number" is embedded in the chip and protected by the use of public key cryptography. The chip also performs some cryptographic operations to authenticate itself without revealing the actual secret information.

I was wondering what are these cryptographic operations that enable a secure financial transaction. I have searched sec.SE and did come across a similar Question but the answers do not explain the workings of the protocol. They focus more on the possible attacks and do not say more than "some crypto math".

I hope I have made myself clear.