The proposition of Bell inequality arises from the exploration of fundamental contradictions between quantum mechanics and classical physics. J. Bell sought to settle the ongoing debates among physicists such as A. Einstein, M. Born, and N. Bohr regarding quantum mechanics, particularly focusing on whether the hypothesis of local hidden variables could account for the physical properties of entangled states. If this hypothesis was valid, it would provide stronger support local realism in classical physics. To test this hypothesis, J. Bell proposed an inequality, known as Bell inequality, which provides an empirical method for verifying the non-classical characteristics of quantum theory.Bell inequality is of paramount importance. Firstly, in the exploration of fundamental physical laws, Bell inequality can be utilized to experimentally verify the non-classicality of quantum mechanics, deepening our understanding of the quantum world and advancing the further development of physics. Secondly, through a thorough investigation of Bell inequality, it is possible to develop more secure and efficient quantum communication technologies, as well as promote the development of fields such as quantum computing and quantum networks.However, explaining Bell inequality is not straightforward. This inequality involves basic concepts such as probability and measurement, employing assumptions like realism and locality that have been ingrained into foundational thinking through classical physics research. Moreover, its mathematical form and derivation process are relatively complex, requiring profound knowledge of mathematics and physics for comprehension. Therefore, establishing an intuitive understanding of Bell inequality can effectively facilitate its research and application.To facilitate a simpler and more intuitive understanding of Bell inequality, this paper provides a review on Bell inequality's intuitive explanation and research progress. This paper is organized as follows: The first part introduces the controversies facing quantum physics and the motivation behind the proposition of Bell inequality. In the second part, we introduce the mathematical form and physical significance of the Bell-CHSH inequality. Specifically, we introduce the concept of the Bell-CHSH inequality, derive the CHSH inequality for continuous hidden variables and discrete hidden variables, derive Bell inequality based on quantum mechanics theory using two specific examples: finding that the product states satisfy the CHSH inequality while the entangled states violate it.In the third part, we analyze why it is said that Bell inequality resolves the debate in quantum physics. We believes that Bell inequality does not solve the problem of whether quantum mechanics is complete, nor does it solve the issue of whether the Copenhagen interpretation is correct. Instead, it provides a criterion for judging whether hidden variable theories can accurately predict experimental phenomena while satisfying realism and locality. If this conclusion holds true, it suggests that further research could be conducted to determine what kind of hidden variables exist, potentially leading to a fundamental replacement of quantum mechanics as the foundational theory.In the fourth part, we introduce two Bell inequalities represented using Venn diagrams. Specifically, based on the assumptions of realism and locality, we use probability theory for inference, geometrically display two sets of Bell inequalities through Venn diagrams, and then introduce entangled states into the inequalities, verifying that entangled states violate Bell inequality.In the fifth part, we introduce the experimental research progress of Bell inequality, including the Wu-Shaknov experiment, Freedman-Clauser experiment, Aspect experiment, Zeilinger experiment, as well as recent experiments on closing detection loopholes, locality loopholes, and free choice loopholes. Finally, we introduce the experimental work of the authors on verifying Bell-CHSH inequality. The sixth part is the conclusion. This paper is expected to help readers gain an intuitive understanding of the important concept of Bell inequality.