When random label noise is added to a training dataset, the prediction error of a neural network on a label-noise-free test dataset initially improves during early training but eventually deteriorates, following a U-shaped dependence on training time. This behaviour is believed to be a result of neural networks learning the pattern of clean data first and fitting the noise later in the training, a phenomenon that we refer to as clean-priority learning. In this study, we aim to explore the learning dynamics underlying this phenomenon. We theoretically demonstrate that, in the early stage of training, the update direction of gradient descent is determined by the clean subset of training data, leaving the noisy subset has minimal to no impact, resulting in a prioritization of clean learning. Moreover, we show both theoretically and experimentally, as the clean-priority learning goes on, the dominance of the gradients of clean samples over those of noisy samples diminishes, and finally results in a termination of the clean-priority learning and fitting of the noisy samples.