Omegle is the logical endpoint of a ubiquitous global network: a single-page website whose sole function is to connect strangers in one-on-one conversation. Upon visiting the site, you are put through to an unseen interlocutor within a few seconds, and then left to do what you will with this temporary channel of communication.
It's Twitter-like in its elegant simplicity, and another of those oh-so-obvious ideas that makes a programmer wince at not having thought of it earlier. And, given the manifold denizens of the net, the outcome of a conversation is entirely indeterminate.
My experiences with it so far have ranged from a pleasant chat with a college student from Derby (on food, education, and getting lost) to a trolling aggressor attempting to cast spells on me ("i summon EPIC INFERNO"); I gather that the system is being put to use for some sort of player vs player game-playing. Another party left rapidly upon discovering that I was not female, simultaneously honouring some equivalent to Godwin's law that states that any online conversation with strangers will inevitably include a mention of paedophilia, lesbians, or 'cyber' (in this case, all three).