Something fitting is perfectly appropriate or proper — it's just right. When someone finds your beloved lost turtle, it's fitting to offer them a reward, or at least a sincere thanks.
If your cousin loves ponies, a pony theme is a fitting choice for his birthday party. As a noun, fitting has a completely different meaning. A clothing fitting is the process of trying on an outfit to see how it fits. A hardware or plumbing fitting is one small piece that fits into a bigger system. The thing all of these definitions have in common is the root word fit.