What is the exact meaning of the word vacuum? Is it just a state of very low pressure or is it nothingness (as in there is nothing)? Also, when we say space is vacuum - it must be referring to pressure as space has light travelling (which means photons) besides the big masses of comets, planets, stars.
Answer
Strictly speaking vacuum is the state of lowest energy. That means no matter or radiation (photons or any other particles).
Note that space is not a perfect vacuum. Also note that, technically, a gas of planets and comets etc. has a pressure (there is usually little reason to care about it though). There is also radiation pressure due to the photons.
People often use the term vacuum loosely to refer to anything less than atmospheric pressure. This is the sense people use when they say space is a vacuum.
EDIT (Re the comments):
Yes, there is a minimum energy. Imagine that you start with vacuum. There is nothing there by definition. Now create some particle. This necessarily takes some energy (at least $mc^2$ where $m$ is the mass of the particle), so the state with a particle in it has more energy. Now the value of the vacuum energy is a subtle thing. Without gravity only energy differences matter, so you can always set the vacuum energy to zero. But with gravity it is tricky, because all energy gravitates. Indeed, physicists now believe that empty space has an energy density, now known as dark energy.
Now people will tell you a big song and dance about quantum fluctuations and zero point energy, but this is only one side of the coin, and only comes in when you try to actually calculate the vacuum energy from a more basic theory (quantum field theory). The basic picture is really simple though: vacuum energy is just a number - some physical constant that we could go out and measure. Now if you check very carefully all the laws we know then you'll find that gravity is the only place the vacuum energy comes in, so for most purposes you can forget about vacuum energy. (People also mention the Casimir effect around this point, but that is another thing entirely.)
On the other question: whether true vacuum is achievable theoretically. Well, it depends what you mean "theoretically." If you mean "in the mind of a theoretical physicist" then sure, it's possible. ;) But if you mean there is some way to build a box and make a perfect vacuum inside of it then no, you can't, because the box will always have some finite temperature and hence blackbody radiation will fill the cavity. You can make it arbitrarily close to true vacuum by cooling the box, but you could never actually reach it.
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