Space is the nickname we use for everything beyond our Earth's atmosphere. It is a good nickname because there is lot of it and it seems relatively empty from our point of view. Doesn't it look like there is a bunch of "space" between the stars in the sky? Don't we know there is a long distance or a lot of space between Earth and other planets, Earth and the Sun or our Solar System and other star systems?
The longer correct name for space depends on where in "space" you are talking about. "Interplanetary space" means the area of space within our solar system, roughly speaking the area from the Sun, in the middle, out to Pluto. Everything beyond Interplanetary space is correctly called "Outer space." (If you imagine your room, where your planets and stars are on the wall as the solar system, it may be easier to imagine the rest of our house as "outer space.")
In one way, space is empty. There is none of the air we need to breathe in space. In many other ways, space is full. There are organic molecules, blackbody radiation left over from the birth of the Universe, gas, plasma, dust, small meteors and space junk -- left over spaceships and trash from astronauts and satellites.