Large language models (LLMs) are moving beyond static uses and are now powering agents that learn continually during their interaction with external environments. For example, agents can learn reusable skills while navigating web pages or toggling new tools. However, existing methods for skill learning often create skills that are over-specialized to a single website and fail to generalize. We introduce PolySkill, a new framework that enables agents to learn generalizable and compositional skills. The core idea, inspired by polymorphism in software engineering, is to decouple a skill's abstract goal (what it accomplishes) and its concrete implementation (how it is executed). Experiments show that our method (1) improves skill reuse by 1.7x on seen websites and (2) boosts success rates by up to 9.4% on Mind2Web and 13.9% on unseen websites, while reducing steps by over 20%. (3) In self-exploration settings without specified tasks, our framework improves the quality of proposed tasks and enables agents to learn generalizable skills that work across different sites. By enabling the agent to identify and refine its own goals, the PolySkill enhances the agent's ability to learn a better curriculum, leading to the acquisition of more generalizable skills compared to baseline methods. This work provides a practical path toward building agents capable of continual learning in adaptive environments. Our findings show that separating a skill's goal from its execution is a crucial step toward developing autonomous agents that can learn and generalize across the open web continuously. Our code can be found in https://github.com/simonucl/PolySkill.