BREAK THE RULES! I thought I should get this one out of the way early. I guess what it boils down to is that there is no simple formula for what makes a good photo. As a bird photographer, you only have a small portion of the latitude of expression of an artist like a painter, but that still leaves a huge number of choices at your discretion. So while tips like mine can be useful in improving your photography, you ultimately should be doing your own thing and figuring out what excites you.
To use this photo of a Helmet Vanga as an example, no decent photographer would recommend shooting a bird in strongly dappled light, with deep shadows and bright sunlight. Generally under these conditions you'd expect a mediocre sort of record shot at best. But this shot breaks the "rules", and at least in my view, is pretty sweet. Something about the way the spots of sunlight illuminate the electric blue bill and brick red mantle communicate the way it actually feels to see this incredible creature in the rainforest understory. I still get a huge shot of adrenaline every time I'm lucky enough to encounter a Helmet Vanga. And if I was going to share a single photo to communicate that experience to someone who had never seen this bird, I'd pick this one, dappled light and all.