Most people consider space to simply be the region above the Earth's atmosphere. But, there is no tangible boundary because the atmosphere gradually thins with increasing altitude. Traces of the gasses we breathe can be found over 100 miles above the earth.
As a comparison, passenger jets cruise at an average altitude of only 30,000 feet (5.7 miles), and the best military jets have a hard time climbing above 100,000 feet (a little less than 19 miles).
So, how do we define where space begins? Many different definitions exist. The United States awards astronaut status to anyone who flies above 50 miles in altitude. Many flight engineers, dealing with the effects of friction and heating of spacecraft due to atmospheric particles, define the boundary to be at 400,000 feet (75.76 miles). They call this the "entry interface," the point at which heating on reentry becomes observable.
Whichever definition you prefer, it is far, far above the level that humans can breathe.