Gravitational attraction is inversely proportional to the square of the distance from the center of gravity of a mass. In theory, there is no "cutoff" or "horizon" where the gravitational attraction of, for instance, the sun, will diminish to precisely zero. This in turn means that all of space is subject to the influence of multiple gravitational fields, even though the force exerted by such fields may be imperceptibly tiny.
The apparent lack of gravitation in space is caused by objects in orbit, for instance, being in a state of free fall. In such a state, the forces acting on the object are uniformly distributed over the object's mass. In an orbiting spacecraft, for instance, both the spacecraft and an astronaut inside it are subject to gravity (otherwise they would stop orbiting and fly off in a straight line). However, the force of gravity is acting uniformly on both the spacecraft and the astronaut and so it cannot be sensed -- it is not, for instance, dragging the astronaut in a certain direction, the way gravity drags a person down on earth.