For the initiated, it's an integrated intelligent software assistant and knowledge navigator functioning as a personal assistant application for iOS.
For the rest of us, it's like the computer on the Starship Enterprise - you know, the one where Kirk asks something and the computer says 'working' and then comes back with a really clever answer about Romulan cloaking technology. I haven't tried going intergalactic with my questions yet but I can talk to my phone in normal, everyday English and it does a fantastic job in writing and sending my texts, setting my alarm and it even reminds me to do stuff when I get home - as long as I've remembered to actually tell the iPhone to remind me in the first place.
I know that a lot of folk have been a bit sniffy about SIRI but I cannot describe the thrill of having some Federation technology in my hands. Or the sheer look of wonder in children's faces when you ask the phone a question like 'why do stars twinkle' and the phone talks back. Magic!