Spiking Neural Network (SNN) is a new generation of artificial neural network with more bio-interpretability, which has the advantages of unique information encoding and processing, rich spatiotemporal dynamics, and low-power event-driven working mode. It has received wide attention in recent years for different areas. The fundamental elements and underlying learning algorithms of SNN are comprehensively introduced. The SNNs classical neuronal model, synaptic plasticity mechanism, especially the information encoding methods, learning algorithms are discussed. An analysis is conducted to explore the strengths and weaknesses of diverse models, highlighting their respective advantages and disadvantages. Finally, the Spiking neural network algorithm of fault diagnosis model with effective neuronal model and synaptic plasticity mechanism is presented with the application scenarios and related potentials. It is expected to further improve the accuracy of equipment fault diagnosis and expand the broader application prospects of artificial intelligence.