Cryptography seems quite an esoteric subject, yet it is fundamental to our world in so many ways. When people think about cryptography, assuming they have heard the word, they will tend to think of 'cloak and dagger' stories, of spies and battles, of secret liaisons amongst lovers and all sorts of high drama.
Of course, there are plenty of examples of this sort of thing in history, from Babington writing in code to Queen mary, to the Allies cracking the German Enigma code, to the Rosenberg trials in the states.
However, cryptography is essential in everyday life. When you buy from a site such as amazon you are relying upon public key cryptography to keep your credit card details safe. When your operating software automatically updates over the internet it too will use a public key algorithm to check that the update it is about to install was really published by the right people, and not by someone trying to get into your computer.
Without cryptography cash machines would not be possible, as the machines would not be able to reliably communicate with the bank computers. Without cryptography, even the idea of electronic voting would not be possible (though they are making a mess of the new systems in the US).
Cryptographic ideas can also be used in making message easier to decode - without these ideas we would not have error checking capabilities on communications lines, and the internet would run much more slowly. We would not be able to reduce redundancy in a message and hence compress it, thus negating popular archival programs such as 'zip'.
All of these ideas, making messages compact, error resistant, secure (or all of the above) are related to cryptography.
Without cryptographic ideas, you would not be able to read this website.