A Markov random field (MRF) is a mathematical model used to represent the joint distribution of a set of random variables with a specific structure. In an MRF, the value of a variable is influenced only by its neighbors, adhering to the Markov property. This local dependency allows for efficient computation and representation of complex systems, such as images or social networks. MRFs are commonly applied in various fields, including computer vision, statistical physics, and machine learning. They help in tasks like image segmentation and spatial data analysis by capturing the relationships between neighboring variables, making them useful for modeling spatially correlated data.