Multi-party dialogue discourse parsing is an important and challenging task in natural language processing (NLP). Previous studies struggled to fully understand the deep semantics of dialogues, especially when dealing with complex topic interleaving and ellipsis. To address the above issues, we propose a novel model DDPE (Dialogue Discourse Parsing with Explanations) to integrate external knowledge from Large Language Models (LLMs), which consists of three components, i.e., explanation generation, structural parsing, and contrastive learning. DDPE employs LLMs to generate explanatory and contrastive information about discourse structure, thereby providing additional reasoning cues that enhance the understanding of dialogue semantics. The experimental results on the two public datasets STAC and Molweni show that our DDPE significantly outperforms the state-of-the-art (SOTA) baselines.