It's about all sorts of stuff relating to being brought up in an Aberdeen supporting family, sharing experiences with them and friends and generally having a deeper understanding of the mentality of the club and it's support through that (and the rivalries that go with it).
Them being my local team helps that, but it's certainly not essential.
You can go a long way with just supporting some random team, but I genuinely believe you are always going to lose out on that last little bit compared to those with deeper ties to a club.