He thinks they're unbelievably important, and says so at great length in his books. But to explain. We call something dissipative if it looses energy to waste-heat. The famous Second Law of Thermodynamics amounts to saying that, if something is isolated from the rest of the world, it will dissipate all the free energy it has. Equivalently, it maximizes its entropy.
Thermal equilibrium is the state of maximum entropy.
In general, however, things are not well-isolated from the rest of the world. If energy arrives from the outside as quickly as it is dissipated, even bodies in the linear regime can be kept away from equilibrium. Thus dissipation, and why dissipative systems are not necessarily dull as dish-water. Even without Prigogine's claims that this theory is Very Significant to biology and social science, even without the philosophical and cultural importance he claims for it, this would be very interesting, and the big question is whether he's right, i.e., whether and to what the theory applies, whether, so to speak, there are Dissipative Structures and not just dissipative structures. This is extreme, but it becomes more plausible the more one looks into the actual experimental literature.