What is Bell's inequality and how does it relate to the concept of quantum entanglement?

Bell's inequality is a mathematical expression that tests the limits of classical physics by examining the correlations between measurements on entangled particles. Quantum entanglement is a phenomenon where two or more particles become connected in such a way that the state of one particle is instantly correlated with the state of another, regardless of the distance between them. Bell's inequality shows that these correlations cannot be explained by classical physics, providing evidence for the non-local nature of quantum entanglement.