The relationship between Cloud and Tifa

[Pivi]

But it's a pretty reasonable theory. It makes sense that (SPOILER)Cloud would want to move on with his life and love, but he's not sure if that's what Aeris wants, so Cloud wants Aeris' forgiveness to "allow" him to move on.

Exactly.

how's Cloud and Tifa relationship described there?

Well, I don't really want to spoil it for You, it's worth a read. You can read it here:
http://xthost.info/ffwebnovel/

But if You want to know, here's the story in a nutshell:
(SPOILER)I'm talking about Case of Tifa now. It shows how Cloud and Tifa started to live together (as friends, not as couple) after the events of Final Fantasy VII, and what did they do then. In the first part, it has some very massive clues that Cloud starts to feel something romantically towards Tifa, at one paragraph he just show a little affection (he's blushing because of that ), so it clearly stated for me, that Cloud's heart do not belongs to only Aerith, but he has some blooming feelings for Tifa too.
But after a while, Cloud got a package from Aerith's "mother" (Cloud's a deliveryboy), and that reminds him of Aerith, and he fell in deep depression. His relationship with Tifa has a big distance from here on, but I really think that Cloud struggles, not only because he remembers Aerith's death, but because he really has some starting feelings for Tifa, and he wants forgiveness from Aerith because of this.
In one part he says that it's his problem, and he wants to settle it alone. Thus he can't settle his feelings with Tifa, because (I think) she's also a little part of his guilt.

But thus, at the ending of Advent Children, Cloud got the forgiveness from Aerith, and he can move on, and I think he won't hold back his blooming feelings for Tifa from this point.
Again, it's just my theory, there's no proof for it (but there's no proof for anything in the movie...).