First, I want a sheath to protect me from the knife should I fall while wearying it. Edge and tip both. Traditionally that used to be done by the placement of rivets and a heavy welt solid spacer that ran from tip to guard. These days it's easily accomplished with synthetics like Kydex.
Second, I want it to allow me to carry the knife securely. That has been done with straps and molding on the sheath for years. The materials may change, but the techniques seem to stay the same.
Third, I want it to carry the knife without damaging the knife (yes, there are sheaths that due to their design and materials can damage your knife by collecting moisture and grit). There's a wealth of options here, but I've become fond of MOLLE strap systems as of late because of their flexibility. Second (nearly equal, perhaps equal, are TekLocs).
Forth, I want the sheath to protect the knife from damage. Some materials and constructions will trap moisture and grit which can damage your blade. Some designs don't allow water to drain. Etcetera, etcetera, etc.
Fifth, I'd like the sheath design to make it easy to get the knife back into the sheath without damaging the sheath. I've had sheaths with straps that were put on "backwards" so that the blade slices the retaining strap as the knife goes back into (and comes out of) the sheath. I've had pouch sheaths that forced the blade to slice the edge of the pouch.
Last, I'd like it to be somewhat attractive. It can be completely utilitarian and still be attractive as long as it's well finished instead of rough and sloppy.