When we can implement this, the implications are huge. You will be able to process large amounts of encrypted data to find broad trends, with out knowing the contents of the encrypted files.
Charles Lickel, vice-president of IBM Software Research, said: "Fully homomorphic encryption is a bit like enabling a layperson to perform flawless neurosurgery while blindfolded, without later remembering the episode."
One of the uses for this that I can see, is doing spam filtering on encrypted email, with out breaking the encryption. So you could broadly publish a private key, and allow everyone to use it - but not open yourself to spam.
Another use would be in large scale data analysis across encrypted and secure clouds. You could (as the cloud provider) mine data about performance from your entire cloud, with out violating any one users privacy.
Companies like Google who depend on relevant, targeted adds could use this to not intrude into your privacy but still deliver the same level of targeting.
Heck - this might be the silver bullet for digital money. People could carry an encrypted file with some digital money in it on a card, and when you swipe the card, the merchant can see if you have enough for the purchase with out seeing your balance.