Are you refering to percolation theory as it relates to electrical conductivity? In that case percolation theory describes the development of long-range connectivity of conductive fillers in your polymer matrix. The percolation threshold would be the critical value related to the probability that an infinite connection has first occured throughout the polymer matrix. When the concentration of filler exceeds this critical value, there is no dramatic change in the conductive properties of the composites. So you can think of the percolation threshold as the minimum weight % of the filler required to achieve a conductive network within your composite.

Dear Ba, percolation theory can be also applied to polymer blends. The percolation threeshold corresponds to the minimum concentration at which the dispersed phase becomes continuous. Probably this can help in understanding the concept. I hope so.

U can apply percolation theory whenever u want to study connectivity i.e., finding the biggest connected chunk of particles, nodes, atoms, islands, whatever u call them. I have seen it being used in chemistry, physics, electrical engineering, oil industry, and even to study the spread of diseases. 

To apply percolation to ur problem u need to specificy whether ur scenario requires discrete percolation (on lattice, octagon and so on) or u have a continuum case. From there u have to link the physics that govern ur medium to the critical density or critical probability and find them in terms of each other.