Percolation theory is a mathematical framework used to study the movement and filtering of fluids through porous materials. It helps in understanding how substances like water or oil flow through soil, rocks, or other media. The theory often involves modeling networks or grids to analyze how connected pathways allow for the spread of fluids or information. This theory has applications in various fields, including physics, biology, and computer science. For instance, it can be used to model the spread of diseases in populations or the flow of electricity in networks. By examining critical thresholds, researchers can predict when a system will transition from a non-flowing to a flowing state.