Deep neural networks (DNNs) are receiving increasing attention in wind power forecasting due to their ability to effectively capture complex patterns in wind data. However, their forecasted errors are severely limited by the local optimal weight issue in optimization algorithms, and their forecasted behavior also lacks interpretability. To address these two challenges, this paper firstly proposes simple but effective triple optimization strategies (TriOpts) to accelerate the training process and improve the model performance of DNNs in wind power forecasting. Then, permutation feature importance (PFI) and local interpretable model-agnostic explanation (LIME) techniques are innovatively presented to interpret forecasted behaviors of DNNs, from global and instance perspectives. Simulation results show that the proposed TriOpts not only drastically improve the model generalization of DNNs for both the deterministic and probabilistic wind power forecasting, but also accelerate the training process. Besides, the proposed PFI and LIME techniques can accurately estimate the contribution of each feature to wind power forecasting, which helps to construct feature engineering and understand how to obtain forecasted values for a given sample.