Could someone explain to me how the Giants won two SB in 4 years?

I've watched of course the freaky plays they needed to beat the Patriots both times but how did they even get there? They were 10 and 9 win teams in the regular season in these runs with ok(ish) seasons the years before and in between,so no juggernauts by any means.

Did they have some particular strength in their team? Did they perform so well in the playoffs? Did the opponents choke? Were they extremely lucky? Did they have some outstanding playmaker(s)? Was Eli so good (I mean he is not considered an elite QB,right)?

It just doesn't add, and since I wasn't watching football back then, could someone inform me?

Edit: I am so surprised this thread got so many respones! I am glad it is an interesting topic for discussion and the answers were very informative!