They're not "rigid" -- they just have a bead that's made of steel wire rather than kevlar fiiber, as the other respondent noted. The only performance difference is a little more weight. Folding tires aren't necessarily easier to install -- that depends on the the fit of tire and rim, and a given kevlar-bead tire can have a tight fit on a given rim. In fact, because the stiffness of the wire bead can help the tire stay on the rim, folding tires often tend to be made a little tighter, and some of them can be hard to install. But you can't generalize.
Higher-performance (and costlier) tires tend to be folders, because people who buy those tend to want the lighter weight.
Wire-bead tires can be folded up a bit, too, if you know how, but they won't make as small a package as the kevlar ones.