Speaking as another long serving individual, the reasons have altered over the years.
My first FNRttC was in 2005. In the 10 years prior to that, I'd mainly been an occasional commuter, but probably since about 2003 I'd started going out more often, doing longer rides, then in 2004 I got a "proper" road bike, and realised that much as I enjoyed heading off to somewhere new, it could be a bit boring. And then on a forum a long, long way from here, I read tales of night time escapes from London, and an early morning secret rendezvous at Gatwick, followed by a fry up by the sea. The quirkiness of the concept of a night ride appealed to me, and I saw it as a way of building up my endurance, and becoming a better, more confident rider. Bear in mind, at the time, I'd never ridden in London, so I wasn't even sure about how to get to HPC! But someone (Arthur) volunteered to chaperone me from the station and that was the start of the FNRttC experience for me.
Back then, I think there was only about 15 people on the ride, so there was no roll-call, no pre-ride speech, not even a "We're on our way!" It was however a complete revelation to me to be riding through the centre of London, with traffic all around, following the wheel in front. I think I really appreciated the essence of the night ride concept once we got out into the countryside, even though at the time I was flagging a bit. The fact that you can be alone and yet be with a group of similar individuals who all have a common aim, both at the same time. I can still remember the feeling of tired elation when we rolled out along the sea front at Brighton, and then posing for a photo shoot. I realised that I wanted to carry on experiencing these things. Later on, I also had other reasons for being out and about, as sadly home wasn't what it used to be, so for a few years until 2011, I viewed the FNRttC as my bit of escapism from somewhere much darker.
Other motivations to carry on doing a night ride, especially in recent years when the ride can have 100+ participants, are helping out at the back, seeing weird sights (Romford nightlife) but also the ability just to have a general chat with friends, about nothing important. All the things User10571 put above, and more.
So as to why a FNRttC, well my explanation is all a bit rambling really, just like the ride itself.
of the premier division of womanhood who probably wouldn't even speak to me in daylight off a bike. 
This was back in early 2008. I'd been a fairly keen, though short-ranged, leisure cyclist in my teens, but had lapsed from that- never took a bike to uni, and never really got back into the habit when that was done with. I'd always commuted by bike after starting work, but apart from that short hop five days a week, my riding was nothing more than the occasional trip to the shops. My interest in cycling for fun started to re-emerge in 2007, at the end of which I got my (now long sold) Dahon Jetstream XP. When I was searching for info & tips on that bike, I came to ACF, found some threads about this Friday Night Ride thing. Hmmm....At the time, my mileage was still in the baby-steps-building-up stage, probably not much more than fifteen or twenty miles a ride, but my interest was piqued. It was something to aim for. Not then, though. I did the IOW Randonnee for the first time that year- just the 50km route, ended up doing 59 miles total that day and my legs were stiff for a few days. Oh, how that's changed....
