Why is there gravity in space?

Newton described gravity as a universal attraction between masses; Einstein reframed it as the curvature of spacetime produced by mass and energy. Either way, the source is the mass. Earth does not pull on things because it has an atmosphere or a solid surface to stand on, so leaving the atmosphere changes nothing about the mechanism. The force falls off with the square of the distance, which means it shrinks quickly but never reaches zero: double your distance from the centre of Earth and you feel a quarter of the pull, not none of it.

At sea level the acceleration due to gravity is about 9.8 m/s2. The International Space Station orbits roughly 400 km up, only a few per cent farther from Earth's centre than the ground is, so the local gravity there is still around 90% of the sea-level value. If the station could somehow be held motionless on a tower that tall and then released, it would fall straight back down.

It floats because it is falling. A spacecraft in orbit moves sideways fast enough that the surface curves away beneath it as quickly as it drops, so it keeps missing the planet. Everything inside - crew, tools, water - falls at exactly the same rate, so nothing presses against anything else and there is no sensation of weight. Gravity is doing all the work; it is simply doing it to everyone equally. The same effect appears for a few seconds in a falling lift, or for half a minute at a time aboard an aircraft flying a parabolic arc.