Question

Why don't satellites in orbit fall to the ground? Why they don't fly off into space?

Answer 1

-- The satellite IS falling, but it never reaches the ground because
it's also moving "sideways" ... in the direction of the orbit ... and
because the Earth is shaped like a sphere.
 
The satellite is moving sideways fast enough so that by the time
it falls 1 foot, the Earth's surface has curved down away from it
1 foot, so it's still the same distance from the Earth's surface.

-- A satellite doesn't fly off into space for the same reason that
a yo-yo doing "around the world" on the end of a string doesn't
fly off ... It's being held onto the circle by the tension in the string,
a force that keeps pulling it toward the center of the circle.

There's a force on the satellite too, that keeps pulling it toward
the center of the Earth.  It's the gravitational force between the
Earth and the satellite.

The satellite doesn't fly off into space for the same reason that
YOU don't do that either.  

Answer 2

They are held in earths gravity.