First one down is money. It's a kind of roundabout point because money is coming from and through the culture, the reason why the MCG is like three times the size of Lords. Basically, there aren't a lot of countries in cricket that can pour as much money into cricket as Australia. The grounds get loads of patrons and the Aussie captain is generally more respected than the head of government. That money means that there are huge facilities like the Centre of Excellence at the Allan Border Field or just the central Academy of Sport, as well as numerous other academies and facilities around the country. More importantly, the money can be afforded to be spent on players as soon as they show any skill. Even a modest talent can afford to be a career cricketer because there is enough money for them to not have to take up another career until they are finished. This sort of thing boxes places like the subcontinent out of contention. The majority of cricketers there can't give 100% because they still need money to come from somewhere else.
The second point that can't be denied is Aussie Rules. The popular winter sport operates in a perfect compliment to cricket. The game is played on cricket fields (meaning cricket grounds are everywhere and usually well maintained) and is helpful in encouraging upper body strength and elite endurance, as well as a focus on catching skills. Even where Rugby League is the dominant sport, the SCG is a prominent football field. There are of course, many carry overs, but one could largely attribute a number of winter sports to them. There is no doubt the England, NZ and SA teams feature very fit players and each have prominent rugby teams, encouraging similar things to Aussie Rules. The main point is that the AFL has driven the importance of cricket stadiums through the roof and made certain that cricket is always a part of the culture.
The third point is simply the competitiveness of the situation. I think simple little things hurt some countries; in South Africa it seems really hard to be a spin bowler, in New Zealand, there just aren't enough people for them to be dominant for a long time and in England the size of the county scene weakens the toughness of the individual teams, where the teams in the top level don't automatically include all of the best players, only the most successful teams (South Africa's franchise system being something I think we will see more and more of).
It's hard to finger a combination, but I wouldn't go too far into weird wishy-washy qualities like "heart" or "teamwork". I think the main effect of Australia is that more of those players who are 'pretty good' make the full distance. They start out a bit rough, but down the track, they have worked and worked until they are as good as the ones who had it all from the start. That is what creates the large pool of talent. For what ever reason, the players just find what they need.