Yang-Mills theory is a mathematical framework that describes how elementary particles interact with each other by exchanging other particles called gauge bosons.

In simpler terms, imagine two friends playing catch with a ball. The ball represents a particle, and the friends represent elementary particles like quarks or electrons. The way the friends catch and throw the ball represents how the particles interact with each other. In Yang-Mills theory, the ball is replaced by a gauge boson, and the friends follow specific rules for catching and throwing the ball that describe the interactions between the particles.

These rules are based on a set of mathematical equations that determine how the gauge bosons interact with each other and with the particles they carry. The theory is important in understanding the behavior of the strong nuclear force, which holds the nuclei of atoms together, and the weak nuclear force, which is responsible for radioactive decay.

Overall, Yang-Mills theory is a way of mathematically describing the fundamental interactions between particles in the universe.