The answer to 'stone walkway turning brown' is that there are several common causes, including dirt buildup, mold/mildew growth, and staining from organic materials. The symptoms include a discolored, unsightly appearance that detracts from the aesthetic of your outdoor space.
In many cases, the solution is a thorough cleaning and sealing of the stone walkway. This can often be done as a DIY project, but for extensive damage or difficult-to-clean areas, it's best to call in a professional landscaping company that specializes in stone maintenance.