Replies up to now have summed it up... it wasn't so much about what he achieved, but how he went about his business. He was always on the absolute limit and he never, ever gave up. For me it's the stories about him little things he would do in and out of the car that sum him up best.
Dr Sid Watkins had great respect for him and said that Gilles's heartrate was always relatively low for a racer, like he was calmer behind the wheel than other drivers. Sid remembers a time when he was in the support car, attending an accident at the Monaco GP. The GP cars had to overtake the support car under yellow flags (this before the days of the F1 pace car of course). All the other drivers went past, giving the support car a wide berth. Gilles came past, lap after lap, as close as he possibly could to the support car without touching it, so that he was on the fastest available line into the corner. He was still giving it ten tenths in those circumstances.
Gilles believed in the "Gap" theory... that is, in any situation in a car, there's always a gap through which you can avoid a crash without stopping. Every situation can be driven around, basically, and braking is essentially a last resort and only required through bad planning. He applied this on the road as well as on track. Sid, in one of his books (can't remember which one) mentions a time he got a lift with Gilles, and was surprised when Gilles's wife offered Sid the front passenger seat. The wife (can't remember her name) then climbed in the back, but instead of sitting on the seat, she lay down on the floor in the footwells and closed her eyes. Sid was confused by this but then Gilles started driving and it all became clear. His hire cars would always return with bent or scratched panels, because when driving on the road, he would still go for the gap - legally or not, and would be happy to bounce off other cars if it would help him maintain momentum, much like we might do in GT4. He'd charge up between two lines of stopped cars at a traffic light at maximum speed, as though he was filtering on a motorbike, to get to the front of a queue. Then he'd jump the light if he could do so with minimal contact.
Jodi once also once said something about living in Monaco being good because it's a 4 hour drive to Nice airport, or 3 and a half hours if you're really quick, and 2 and half hours if you're Gilles Villeneuve, or something like that. I could have the times and locations wrong, but Gilles's commuting time (in a Ferrari 308) has become legend.
Gilles died when, flat out on a qualifying lap and determined to beat team mate Pironi, he came across a slower car. Instead of backing off and sacrificing the lap, he went for the gap. A true racer to the end, and one gifted with total self belief and supreme car control.
