To directly answer your question, GoreTex doesn't actually breathe. It is a membrane that is laminated to a synthetic material. The membrane is actually full of millions of little holes that are large enough for air to get through but too small for water to pass.
How breathable is GORE-TEX active?
GORE-TEX active garments are designed for fast-paced, high-aerobic, done-in-a-day activities even in bad weather. They're totally windproof, extremely breathable, can easily be packed away and come with the GUARANTEED TO KEEP YOU DRY™ promise.
Is GORE-TEX really breathable?
Because the GORE-TEX membrane is also breathable, and windproof. No matter if you're speeding down a mountain bike trail, running along the coastline, or walking home between tall skyscrapers on a winter night, the wind simply can't get through to chill you.