The best explanation I've read of the terms yapp and semi-yapp comes from R. L. Allan's Nicholas Gray, which you can read here: "Meaning of Yapp." Long story short, think of yapp as the edge of the cover. A semi-yapp cover will wrap around the page edges, while a full-yapp cover wraps even farther, to the point of touching or thereabout. Imagine an old-style zippered Bible minus the actual zip. Or better yet, just look at this picture:
There are two factors at work here: the extension of the cover, and the curve. A full- or semi-yapp cover is not simply one that extends out past the edge of the paper. It also curves around, as if to cup the book block in its leather embrace. The Bible in the photos, an R. L. Allan ESV Compact Text Edition, gets things just right. When executed well, a semi-yapp edge adds some Old World elegance to a Bible.
When you compare the Bible to the hardback journal underneath, you can see how a semi-yapp cover delivers practical benefits. Not only does it feel nice in the hand, but it also offers protection to the gilded page edges. On a small Bible like this, I find it particuarlly attractive ... but in all honestly, I like semi-yapp in any size cover.
The downside? Some people find that the extra leather around the edge of the cover gets in the way when flipping pages. I haven't had much trouble in that regard -- but I don't often rush from text to text (on principle, not just because I'm slow). Your mileage may vary, so be advised.