The public key is used to do the encrypting, and the private key is used to do the decrypting. This allows two parties to exchange information over a plaintext, unsecured channel without ever meeting or exchanging secrets out of band. The recipient can generate a keypair, send the public key over the insecure channel, and wait for the sender to encrypt something using it. At this point, only the recipient — the holder of the private key — can decrypt the data.

Although there are a few different public-key encryption algorithms, the most popular — and fortunately, the easiest to understand — is the RSA algorithm, named after its three inventors Rivest, Shamir and Adelman. To apply the RSA algorithm, you must find three numbers e, d and n related such that ((m^e)^d) % n = m. Here, e and n comprise the public key and d is the private key. When one party wishes to send a message in confidence to the holder of the private key, he computes and transmits c = (m^e) % n. The recipient then recovers the original message m using m = (c^d) % n.

Reference:
http://commandlinefanatic.com/cgi-bin/showarticle.cgi?article=art012