What the hell is it?
Luthite is a proprietary composite material developed by Ibanez Guitars specifically to build electric stringed instruments of. It is used in the company's Ergodyne line of basses and EDR line of guitars, and not really in any other Ibanez instruments. It has been licensed to a number of other manufacturers, for example Cort's Curbow basses feature Luthite bodies.
What is it good for?
The main feature of Luthite appears to be the fact that, unlike wood, it can be shaped into nearly any form imaginable without the process being prohibitively expensive. Thus, the Ergodyne basses look like something taken out of some Star Wars cantina scene (the Cort Curbow basses look more traditional, you could even call them stylish). Indeed, most Luthite-made basses look and feel as if they are way more expensive than they actually are. The material is extremely durable, which is a good thing, since bass players tend to be the band members who put up the strangest acts on-stage (possibly to compensate for the fact that nobody listens to them anyway; the Path of the Bassist is a difficult and unforgiving one to tread). As for the guitars, they have a much more conservative design, so they don't really use this feature of the luthite material convincingly.
Is it any good?
Having played a little around with an Ergodyne EDA900 bass, I was mostly surprised about the weight of the thing. Even my own very light bass (made of agathis wood, because I'm a cheapskate) was more uncomfortable for the back than this thing. Another pro for bass players who like to jump around and pretend they're Flea; they won't break their backs while doing so. It's said to be engineered for sonic properties (like resonance and sustain) as much as weight and the look factor, although this is really hard to judge, since Ibanez does not manufacture other instruments with the same electronics as the Ergodynes and EDRs. It is said (now THAT'S a reputable source) to have sonic properties that come closest to those of maple. Several players of Luthite-made instruments remark that the material exudes a horrible stench (of "new plastic") which takes about a week to wear off. The exact components of the material appear to be a trade secret.
Is it better than wood?
The jury's still out on that one. It's lighter and easier to shape, that much is for sure. Some musical instrument audiophile types can reliably tell the difference between a nut made of bone and one made of graphite, or worse, plastic, so I wouldn't be surprised if those freaks would claim that some expensive boutique wood (like, say, the old favourite for musical instrument production, mahogany) has better resonance. I wouldn't be surprised if they were right, either.
As a side note, Ibanez' Luthite isn't the first example of man-made materials for musical instruments. Steinberger's entire 1980's product line was made of "Steinberger Blend", another proprietary material. It consisted mainly of carbon, graphite, Kevlar, fibreglass and epoxy, and it would be likely that Luthite has those (or some of) those components as well.