While large language models (LLMs) have demonstrated superior multi-task capabilities, understanding the learning mechanisms behind this is still a challenging problem. In this paper, we attempt to understand such mechanisms from the perspective of neurons. Specifically, we detect task-sensitive neurons in LLMs via gradient attribution on task-specific data. Through extensive deactivation and fine-tuning experiments, we demonstrate that the detected neurons are highly correlated with the given task, which we term as task-specific neurons. With these identified task-specific neurons, we delve into two common problems in multi-task learning and continuous learning: Generalization and Catastrophic Forgetting. We find that the overlap of task-specific neurons is strongly associated with generalization and specialization across tasks. Interestingly, at certain layers of LLMs, there is a high similarity in the parameters of different task-specific neurons, and such similarity is highly correlated with the generalization performance. Inspired by these findings, we propose a neuron-level continuous fine-tuning method that only fine-tunes the current task-specific neurons during continuous learning, and extensive experiments demonstrate the effectiveness of the proposed method. Our study provides insights into the interpretability of LLMs in multi-task learning.