A number of things can be meant by it. What is never meant by it is a distinct denomination or ecclesiastical body. It is a wing of the Anglican tradition which emphasizes the more Catholic elements of Anglicanism. It’s a somewhat broader and vaguer term than “Anglo-Catholic,” though it’s often used to mean much the same thing. “High Church” usually means an emphasis on traditional liturgy, a high valuation of the sacraments, a strong view of the authority of the Church and of the priestly office, etc. I would define an Anglo-Catholic more precisely, as an Anglican who accepts without reservation the authority of the Seven Ecumenical Councils and the tradition of the first-millennium Church in general, and accepts only those portions of the Reformation as can be reconciled with that tradition. (Generally a true Anglo-Catholic will also treat the medieval Western councils with considerable respect, and will pay a certain deference even to the utterances of the post-Reformation “Roman Catholic” Church.) One may have a taste for “high church” liturgy and even doctrine without being willing to go quite so far.
I am very close to Anglo-Catholicism, but not quite there. I would say that I generally follow the Seven Councils and the first-millennium Church, but I wouldn’t embrace them without hesitation. I remain Anglican largely because I think the Reformation did have some value. I hope that the Reformation can be interpreted in the light of the “undivided Church,” but I think its critiques need to be listened to very carefully rather than simply rejected where they differ from what Catholics and Orthodox have in common (which is another way of defining Anglo-Catholicism). At the end of the day if you force me to choose between the Reformation and the first-millennium Church, I’ll choose the latter. But I’d rather put the two into dialog and see what new insights might emerge. And Anglicanism is a place where that dialog can happen.
Edwin