Percolation is a mathematical concept describing a random arrangment which happens to make a connected network.   In nanotechnology, percolation is used in conductive composite materials containing a random arrangment of SWNTs.   Imagine a 2-dimensional plane of a composite's polymer matrix in which SWNTs are mixed and dispersed.   Some of the nanotubes will form connections and some will not.  


The percolation threshold in this case would be the number of nanotubes it takes to form an electrical connection across the material.   Percolation thresholds are usually expressed in terms of a ratio or percentage by weight of the fiber (i.e. the nanotubes) and its hosting matrix.   A lower threshold indicates that less nanotubes are required to create an electrical connection.   A higher threshold means that a connection is more likely to occur, but the cost of the material will be higher.