Good question. Anglicans don't believe anything that many other Christians couldn't also believe in--Bible, Nicene Creed, Baptism, Eucharist, threefold ministry of bishops, priests, deacons. Hardly distinctive or controversial.
It's how that has worked out that is important. There is a lot of yakking about Anglican Christianity being both 'catholic and evangelical' (or 'reformed'), and stuff about the via media. But that can end up sounding a lot like it's a meeting-in-the-middle so that you don't offend anyone, and you don't hold anything particularly strongly.
But that's not what I think that 'catholic and evangelical' means, really. As MC Hammer said, 'breakitdownnow'. Let's get to the core meanings of those two words.
'Catholic'--universal, found everywhere.
'Evangelical'--describes 'good news'.
Yikes. The 'good news that is found everywhere.' A tall order, indeed.
So, a church that is catholic and evangelical is the church that gives the SAME good news in all places, by BEING the RIGHT good news for EACH place.
To me, this implies a commitment to place. And this is well-founded in our history. Augustine was sent by Gregory the Great to evangelise the English, and was told to adapt to the local customs, whether the somewhat debased Christianity that existed, or whatever habits of mind and heart he found that could be genuinely in tune with the Gospel. You do what is right for the place, and marry it up with the fullness of the Gospel. You meet the needs of the people. You persuade, rather than coerce. You do, more than you say.
Okay, that's the first baby-steps reflection.