Recent breakthroughs in multimodal large language models (MLLMs) have endowed AI systems with unified perception, reasoning and natural-language interaction across text, image and video streams. Meanwhile, Unmanned Aerial Vehicle (UAV) swarms are increasingly deployed in dynamic, safety-critical missions that demand rapid situational understanding and autonomous adaptation. This paper explores potential solutions for integrating MLLMs with UAV swarms to enhance the intelligence and adaptability across diverse tasks. Specifically, we first outline the fundamental architectures and functions of UAVs and MLLMs. Then, we analyze how MLLMs can enhance the UAV system performance in terms of target detection, autonomous navigation, and multi-agent coordination, while exploring solutions for integrating MLLMs into UAV systems. Next, we propose a practical case study focused on the forest fire fighting. To fully reveal the capabilities of the proposed framework, human-machine interaction, swarm task planning, fire assessment, and task execution are investigated. Finally, we discuss the challenges and future research directions for the MLLMs-enabled UAV swarm. An experiment illustration video could be found online at https://youtu.be/zwnB9ZSa5A4.