The Secret Path is a hidden route that can be visited in Nintendogs + Cats. It is usually very rare and appears more often if the player has at least 5,000 Owner Points. It is a path that can be found anywhere within the four routes (Seaside, Mountains, Downtown, and Neighbourhood/Town).
The secret path sign will be on the left-hand side of the screen on the Downtown, Mountains, and Neighborhood routes, and it will be on the right-hand side on the Seaside route. On the route many gifts and traffic cones can be found, or more grass patches than usual if the Secret Path is taken from the Town or Mountain routes. If it says, "Your dog seems anxious" at the beginning of the walk, the Secret Path is most likely in one of the routes.
Also, if it says, "You might want to keep going a little longer than usual" then just stay on the same path, because it is very likely that the secret path is somewhere ahead. It can also say "Feel like dropping by someplace?" which is another sign that the secret path is (maybe) somewhere ahead.