Answer:
The fundamental limitation of symmetric (secret key) encryption is ... how do two parties (we may as well assume they are Alice and Bob) agree on a key? In order for Alice and Bob to communicate securely they need to agree on a secret key. In order to agree on a secret key, they need to be able to communicate securely. In terms of the pillars of IA, To provide CONFIDENTIALITY, a secret key must first be shared. But to initially share the key, you must already have CONFIDENTIALITY. It's a whole chicken-and-egg problem.
This problem is especially common in the digital age. We constantly end up at websites with whom we decide we want to communicate securely (like online stores) but with whom we there is not really an option to communicate "offline" to agree on some kind of secret key. In fact, it's usually all done automatically browser-to-server, and for the browser and server there's not even a concept of "offline" — they only exist online. We need to be able to establish secure communications over an insecure channel. Symmetric (secret key) encryption can't do this for us.
Asymmetric (Public-key) Encryption
Yet one more reason I'm barred from speaking at crypto conferences.
xkcd.com/177/In asymmetric (public key) cryptography, both communicating parties (i.e. both Alice and Bob) have two keys of their own — just to be clear, that's four keys total. Each party has their own public key, which they share with the world, and their own private key which they ... well, which they keep private, of course but, more than that, which they keep as a closely guarded secret. The magic of public key cryptography is that a message encrypted with the public key can only be decrypted with the private key. Alice will encrypt her message with Bob's public key, and even though Eve knows she used Bob's public key, and even though Eve knows Bob's public key herself, she is unable to decrypt the message. Only Bob, using his secret key, can decrypt the message ... assuming he's kept it secret, of course.
Explanation:
