As the amount of life spent online continues to increase, a great deal of private information is naturally being transmitted: banking details, medical records, business correspondences. Where once these exchanges of data would have occured between a small set of individuals in a shared space, they now happen between continents, through hundreds of servers and over complex network infrastructures. It is a system that cannot be fully accounted for by any individual, and so the means of transmission are insecure--much like having a letter transmitted by a series of couriers, the data is liable to be intercepted or modified. And so both parties in the exchange take on a risk that may prohibit especially critical data from being sent. Cryptography is the study of data obfuscation--a means of making a message readable only by some. It is the answer to the question "when the means of transmission cannot be trusted, how can information be conveyed securely?
There are two classes of encryption: symmetric and asymmetric. Symmetric encryption allows a message to be encoded and decoded with the same piece of information, or key. The ancient Caesar cipher is an example of this; an arbitrary number acting as the key was agreed upon by both parties, and every letter in the message was shifted through the alphabet by that amount. It could easily be decoded by anyone who knew the key by simply shifting the letters backward through the alphabet. Simple algorithms such as the Caesar cipher are vulnerable to various attacks due to the patterns that they create in the ciphertext. A given letter may always be encoded in the same way, meaning that the key could be compromised if the attacker gained access to the plaintext and ciphertext forms of the same message. And a message could be decrypted without the key by recognizing repeated patterns in the ciphertext representing common words. More advanced symmetric encryption methods--like the Advanced Encryption Standard (AES) algorithm, developed for the US National Institute of Standards and Technologies--disrupt patterns in the message to prevent these types of attacks.
Symmetric encryption is an imperfect solution in the internet age. Because it requires both parties to know the same secret key, those parties must have a secure form of communication already established. In the days of Caesar, this key exchange could be performed confidentially by two individuals in close proximity. When encryption is used on the internet, it cannot be assumed that the communicating parties will have had any physical interactions--and it would be impractical to expect every new customer of an online banking service to perform a physical key exchange. Asymmetric encryption solves this problem by removing the key exchange. Instead of encrypting and decrypting a message with the same key, an asymmetric encryption algorithm has a keypair, comprising a public key, used for encrypting a message, and a private key, used for decrypting a message. The keys are so named because the private key is never shared, while the public key can be broadcast widely.
Typically, it demands more processing power to encrypt and decrypt messages with an asymmetric encryption implementation than a comparable symmetric one. For this reason, it is desirable to use symmetric encryption for most communications. An asymmetric implementation such as the Rivest--Shamir--Adleman (RSA) system is used to perform the key exchange. One of the devices will broadcast its public RSA key to the other, which will respond by generating an AES key, encrypting it with that RSA key, and returning it. This method of key exchange is secure, even if every network packet is intercepted. Once the devices share an AES key, they can communicate with the more efficient symmetric encryption method.