Here's something to give you an idea of how big space is. It takes about an eighth of a second for light to go around the Earth once, but it takes four years for it to reach us from the nearest star.
Let's reduce the 12,000 km diameter earth to the size of a quarter--2 cm wide. On that scale, Alpha Centauri, which is a bit over 40 trillion km away, would still be a whopping 70,000 km away!
Now, let's reduce the Earth's entire orbit around the Sun--about 300 million km diameter--to the size of a quarter. On that scale, Alpha Centauri is still 130 km away!
Let's take this one step further and reduce the entire Solar System out to Neptune's orbit down to quarter-size. That's a radius of about 35 AU. Even at that scale, Alpha Centauri would be four kilometers away!
Now, to get an idea of how empty all that space is, let's compress all the matter in the universe into a single mass with the same density as the Sun. The observable universe is estimated to have a mass of about 10^22 times that of the Sun. We'll ignore the fact that anything over three solar masses normally collapses into a black hole unless it's undergoing fusion as a star, and let's just lump all of this matter together into a single big mega-star with the same density as our Sun. That mega-star would have a diameter of just over 20 million times that of our Sun--about 30 trillion km, or just under three light-years in diameter! Yes, you heard right: all of the matter in the known universe, compressed into a ball with the same density as our Sun, would have a diameter less than the distance between our Sun and its nearest neighbor!
To put this in scale with the diameter of the universe, let's assume that the universe stretches out to the cosmic horizon (14 billion light years away) and no farther (it may be bigger but we can't see beyond the cosmic horizon because the universe is too young for light to have reached us from there yet). Reduce this vast space to the size of the Earth. At that scale, our mega-star with all of the matter in the universe contained in it, would be a BB, five millimeters in diameter. Imagine that--the universe as a completely empty space the size of Earth, and all of the matter contained in it is just a BB pellet.