The blind method is used for serged diapers - you have your inner and outer layers rightsides out, place the elastic between the layers, then sew with a 3-step zig-zag all the way down the elastic (but you can't see it because it's under a body piece - you have to feel where it is). For serged diapers, you can also sew the elastic to just the inside or outside body piece. I've only done outside body piece. I plan to try the blind method soon.
Pros/cons of different methods...
Serged diaper methods...
Blind - keeps your serged layers together nicely so it's not as poofy, and I think Amber said it can give a tighter leg and hold stuff in better? I don't have a diaper sewn this way, so I'm not sure

It's harder to sew this method, since you can't see the elastic, but it's easier to serge the diaper afterward, since all body layers are equally elasticized.
Sewing to either body layer of a serged diaper - This is easier to sew, but then it's more tricky to serge.
T&T diaper methods...
Casing with elastic tacked down at either end - This gives a nice gather because the elastic is "free" in the casing. It can be a pain to sew, because you either have to tack down the ends, then hold the elastic out of the way while sewing the casing. Or you have to sew the casing before tacking down (you can thread it through or have it tacked on one side only as a PP mentioned), and that all requires lots of turning back and forth. Some people experience wicking through casing stitches. I've not experienced this, but if you have a heavy wetter, you might look into another method or spray the casing with DWR waterproofing spray.
Casing with elastic sewn to the seam allowance - This is very easy to do - just sew it to the seam allowance, turn it out, then sew the casing without catching the elastic. The elastic is sewn into place, so it's easy to not catch it.

Again, you have the possible wicking factor for heavy wetters.
No-casing with elastic sewn to seam allowance - Here you want the leg to roll in or out, depending on your materials. The downside to this is that sometimes it's harder to get the leg to consistently roll the correct direction, and that would require tucking in (or out). You can cut the PUL bigger than the internal body layers, and you can also sew the 3-step zig-zag without sewing the seam closed first - someone posted this method the other day and got great results with it. I haven't tried it yet. So far, I've found that cutting the PUL bigger works pretty well if it's "bigger enough".

And one more method I think I saw in HHs... Don't they have the elastic tacked down on both ends with no casing and no sewing it to the seam allowance? I *think* that's how they're done, but I only had one very briefly, and I wasn't making diapers yet, so I didn't study the construction that long.

I personally like the look of a casing, and I think it works pretty well for my child. But everyone has their own preferences! For serged diapers, I tend to sew to the outside body only, but I'm going to try the blind method next time and see IF I can do it.
