Drug synergy, characterized by the amplified combined effect of multiple drugs, is critically important for optimizing therapeutic outcomes. Limited data on drug synergy, arising from the vast number of possible drug combinations and testing costs, motivate the need for predictive methods. In this work, we introduce CongFu, a novel Conditional Graph Fusion Layer, designed to predict drug synergy. CongFu employs an attention mechanism and a bottleneck to extract local graph contexts and conditionally fuse graph data within a global context. Its modular architecture enables flexible replacement of layer modules, including readouts and graph encoders, facilitating customization for diverse applications. To evaluate the performance of CongFu, we conduct comprehensive experiments on four datasets, encompassing three distinct setups for drug synergy prediction. CongFu achieves state-of-the-art results on 11 out of 12 benchmark datasets, demonstrating its ability to capture intricate patterns of drug synergy. Through ablation studies, we validate the significance of individual layer components, affirming their contributions to overall predictive performance. Finally, we propose an explainability strategy for elucidating the effect of drugs on genes. By addressing the challenge of predicting drug synergy in untested drug pairs and utilizing our proposed explainability approach, CongFu opens new avenues for optimizing drug combinations and advancing personalized medicine.