Low Earth orbit (LEO) satellite plays an indispensable role in the equal access network because of its low latency, large capacity, and seamless global coverage. For such an unprecedented extensive irregular system, stochastic geometry (SG) is a suitable research method. The SG model can not only cope with the increasing network scale, but also accurately analyze and estimate the network's performance. Several standard satellite distribution models and satellite-ground channel models are investigated in this article. System-level metrics such as coverage probability and their intermediates are introduced in the non-technical description. Then the influence of gateway density, and the number and height of satellites on latency and coverage probability is studied. Finally, this article presents the possible challenges and corresponding solutions for the SG-based LEO satellite system analysis.