Matching things look exactly alike. A pair of leather boots is matching, and if you and your sister wear matching outfits, they're identical.
One way to use matching is to mean "exactly the same," so if a company donates matching funds to a charity, it gives exactly the same amount as other donors — it matches, or duplicates, the amount. Other matching things simply go together, or are coordinated: "The baby looked so cute in his little snowsuit and matching hat."