Recommender systems are central to digital platforms, yet they face a fundamental trade-off between accuracy and explainability. Black-box models achieve strong performance but lack interpretability needed for trust and adoption. Existing explainable AI approaches either treat explanations as post-hoc or at the cost of accuracy. We challenge this view, proposing that explanations, when designed as an integral component of a system and aligned with prediction outcomes, can improve both interpretability and performance. We introduce RecPIE (Recommendation with Prediction-Informed Explanations), a framework that jointly optimizes recommendation predictions and natural-language explanations generated by LLMs. RecPIE embeds explanation generation into the learning loop: predictions guide explanation generation (prediction-informed explanations), which are fed back to refine subsequent predictions (explanation-informed predictions) via alternating training. The LLM is fine-tuned using LoRA and reinforcement learning with a customized reward derived from recommendation accuracy. Drawing on multi-environment statistical learning theory, we formally ground why explanation generation and prediction can be mutually reinforcing. We evaluate RecPIE on large-scale point-of-interest recommendation data from Google Maps, where user preferences span diverse place categories. RecPIE improves predictive accuracy by 3-4% over state-of-the-art baselines and matches the best performing model using only 12% of the training data. In human evaluations with 566 participants, RecPIE explanations are preferred 61.5% of the time (versus 16.6% for the best baseline) and rated closer to human-generated explanations. These results reframe explainability not as a constraint on performance but as a design lever for improving AI systems, with implications for trust, data efficiency, and marketplace deployment.