In truth, we don’t really know how big space is. We know that at the big bang, 10 billion years ago, all the universe was squashed into one point. Then it expanded (the big bang), and has been expanding ever since. Certainly, there are at least millions of galaxies out there, each like our own, and there is probably intelligent life out there somewhere.
Scientists are still debating whether the universe will keep expanding forever. If there is enough mass in the universe, then the force of gravity will force the universe to come back together again, leading to a ‘big crunch’. Alternatively, if there is not enough mass, the universe will keep expanding forever, until everything is so spread out that no stars or planets can exist. We can’t yet measure how much mass there is in the universe, so we don’t know what our ultimate fate will be. Of course, the human race, the earth and even our own solar system will no longer exist well before we have to worry about this.