Barefoot walking and grounding mats share the same idea: a direct connection between your skin and the earth. They just get there in different ways.
Barefoot walking
Grass, sand, and bare soil are the original way to ground. It's free and it gets you outside. The catch is time and weather: most of us can't spend hours barefoot outdoors, especially in winter or in a city.
A grounding mat
A grounding mat brings the connection indoors. Its cord plugs into the ground port of a grounded outlet, which is wired to the earth. Put it under your desk or on the sofa, and you stay connected for as long as you sit there.
Which one should you choose?
You don't have to choose. Many people walk barefoot when they can, and use a mat for the hours they spend indoors.